J P Mohindru and Bharat Mohindru Solutions for Chapter: Introduction to Trigonometry, Exercise 9: CHAPTER TEST

If $\mathrm{\pi }\le \mathrm{\theta }\le \frac{3\mathrm{\pi }}{2}$, then $\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}+\sqrt{\frac{1-\cos \theta }{1+\cos \theta }}$ is equal

If $0°<\theta <90°$, find $\theta$ when $2 \cos \theta +2\sqrt{2}=3 \sec \theta$

If $\tan \theta +\sin \theta =a$ and $\tan \theta -\sin \theta =b$, what is the value of $(a^2-b^2)÷\sqrt{ab}$

If $\lambda \cos \theta =1$ and $\lambda \sin \theta =\sqrt{3}$, find the positive value of $\lambda$.

Write the value of ${\cot }^2\theta -{\mathrm{cosec}}^2\theta$.

If $5\cot A=8,$ and the value of $\sec A=\frac{\sqrt{x}}{8}$, then find the value of $x$.

If $cot\theta =\frac{15}{8}$, find the value of: $\left(\frac{\left(2+2\sin \theta \right)\left(1-\sin \theta \right)}{\left(1+\sin \theta \right)\left(2-2\cos \theta \right)}\right)$

Prove that: $\left(1-\cos \theta \right)\left(1+\cos \theta \right)\left(1+co{t}^2\theta \right)=1$.