Find $$\(\int \frac{1}{(5 \sqrt{3} \cos 3 \theta+5 \sin 3 \theta)^{2}} d \theta\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m21_qp_22 Year：2021 Question No：7(c)
Answer:
State integrand of form \(k_{1} \sec ^{2}\left(3 \theta-\frac{1}{6} \pi\right)\)
Integrate to obtain form \(k_{2} \tan \left(3 \theta-\frac{1}{6} \pi\right)\)
Obtain \(\frac{1}{300} \tan \left(3 \theta-\frac{1}{6} \pi\right)+c\)
Integrate to obtain form \(k_{2} \tan \left(3 \theta-\frac{1}{6} \pi\right)\)
Obtain \(\frac{1}{300} \tan \left(3 \theta-\frac{1}{6} \pi\right)+c\)
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
2.3.2.2 the expansions of
2.3.2.3 the formulae for sin 2A,cos 2A and tan 2A
2.3.2.4 the expression of
Solution:
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