θ - θ - 2 2θ - 4 4θ =

Correct Answer is : 8cot⁡8θ8 8θ8cot8θ

Correct Answer is : 8cot⁡8θ8 8θ8cot8θ

Test Index

TS EAMCET 4 May 2018 Shift 2 Solved Paper

Section: Mathematics

Question : 22 of 160

Marks: +1, -0

\cot \theta - \tan \theta - 2 \tan 2\theta - 4 \tan 4\theta =

Solution:

Consider the expression,

\cot \theta - \tan \theta - 2 \tan 2\theta - 4 \tan 4\theta

Simplify the above,

\frac{\cos \theta}{\sin \theta} - \frac{\sin \theta}{\cos \theta} - 2 \frac{\sin 2\theta}{\cos 2\theta}

-4 \frac{\sin 4\theta}{\cos 4\theta}

=2 \frac{\cos^{2}\theta - \sin^{2}\theta}{2 \sin\theta \cos\theta} - \frac{\sin 2\theta}{\cos 2\theta}

-4 \frac{\sin 4\theta}{\cos 4\theta}

=2 \frac{\cos^{2}\theta - \sin^{2}\theta}{2 \sin\theta \cos\theta} - 2 \frac{\sin 2\theta}{\cos 2\theta}

-4 \frac{\sin 4\theta}{\cos 4\theta}

=2(2) \frac{[\cos^{2}2\theta - \sin^{2}2\theta]}{2 \sin 2\theta \cos 2\theta}

-4 \frac{\sin 4\theta}{\cos 4\theta}

= \frac{4\cos 4\theta}{\sin 4\theta} - 4 \frac{\sin 4\theta}{\cos 4\theta}

Further simplify the above,

4 \left[ \frac{\cos^{2}4\theta - \sin^{2}4\theta}{\sin 4\theta \cos 4\theta} \right] = 8 \frac{\cos 8\theta}{\sin 8\theta}

=8 \cot 8\theta

Go to Question:

Prev Question

Next Question