K. C. Sinha Solutions for Chapter: Trigonometric Functions (Sum and Difference of Angles and Transformation Formulae), Exercise 1: EXERCISE 3.1

Find the value of: $\cos 1395°$

Find the value of: $\tan \left(\frac{11\pi }{12}\right)$

Find the value of: $\tan \left(\frac{13\pi }{12}\right)$

Prove that $\cos 9°+\sin 9°=\sqrt{2}\sin 54°$

prove that

$\tan 9°+\tan 36°+\tan 9°\tan 36°=1$

Prove that

$\sin \left(A+B\right)\sin \left(A-B\right)+\sin \left(B+C\right)\sin \left(B-C\right)+\sin \left(C+A\right)\sin \left(C-A\right)=0$

Prove that

$\tan \left\{\left(2n+1\right)\pi +\theta \right\}+\tan \left\{\left(2n+1\right)\pi -\theta \right\}=0$

If $\alpha$ and $\beta$ are the solutions of the equation $a\cos \theta +b\sin \theta =c$, then show that

$\cos \left(\alpha -\beta \right)=\frac{2c^2-\left(a^2+b^2\right)}{a^2+b^2}$