Question

Value of 'x' from the equation $cosec({90}^o-\theta )-x^{3}sin({90}^o-\theta )tan({180}^o+\theta )=sin({90}^o+\theta )$ is

• A. $sin\theta$
• B. $cos\theta$
• C. $tan\theta$
• D. $sec\theta$

Answer 1

Answer: (C)

$tan\theta$

$\csc (90-\theta )-x^3\sin (90-\theta )\tan (180+\theta )=\sin (90+\theta )$

$\Rightarrow \sec \theta -x^3\cos \theta \cot \theta =\cos \theta$

$\Rightarrow x^3\cos \theta \cot \theta =\sec \theta -\cos \theta$

$\Rightarrow x^3\cos \theta \cot \theta =\frac{1}{\cos \theta }-\cos \theta$

$\Rightarrow x^3\cos \theta \cot \theta =\frac{1-{\cos }^2\theta }{\cos \theta }$

$\Rightarrow x^3\cos \theta \times \frac{\cos \theta }{\sin \theta }=\frac{{\sin }^2\theta }{\cos \theta }$

$\Rightarrow x^3=\frac{{\sin }^3\theta }{{\cos }^3\theta }={\tan }^3\theta$

$\therefore x=\tan \theta$