Solve the equation $$\(7 \cot \theta=3 \operatorname{cosec} \theta\)$$ for $$\(0^{\circ}<\theta<90^{\circ}\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w20_qp_22 Year：2020 Question No：1
Answer:
Use $\cot \theta=\frac{\cos \theta}{\sin \theta}$ and $\operatorname{cosec} \theta=\frac{1}{\sin \theta}$
Simplify to obtain $\cos \theta=k$ where $0<k<1$
Obtain $\cos \theta=\frac{3}{7}$ and hence $\theta=64.6$ and no other solutions in the range
Alternative method for question 1
Use identity $\operatorname{cosec}^{2} \theta=1+\cot ^{2} \theta$
Simplify to obtain $\tan \theta=k_{1}$ or $\sin \theta=k_{2}$ where $0<k_{2}<1$
Obtain $\tan \theta=\frac{1}{3} \sqrt{40}$ or $\sin \theta=\frac{1}{7} \sqrt{40}$ and hence $\theta=64.6$ and no other solutions in the range
Simplify to obtain $\cos \theta=k$ where $0<k<1$
Obtain $\cos \theta=\frac{3}{7}$ and hence $\theta=64.6$ and no other solutions in the range
Alternative method for question 1
Use identity $\operatorname{cosec}^{2} \theta=1+\cot ^{2} \theta$
Simplify to obtain $\tan \theta=k_{1}$ or $\sin \theta=k_{2}$ where $0<k_{2}<1$
Obtain $\tan \theta=\frac{1}{3} \sqrt{40}$ or $\sin \theta=\frac{1}{7} \sqrt{40}$ and hence $\theta=64.6$ and no other solutions in the range
Knowledge points:
2.3.1 understand the relationship of the secant, cosecant and cotangent functions to cosine, sine and tangent, and use properties and graphs of all six trigonometric functions for angles of any magnitude
2.3.2.1 more contents
Solution:
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