H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Introduction To Trigonometry, Exercise 5: REVISION EXERCISE

Evaluate 
$\sin \left(50°+\theta \right)-\cos \left(40°-\theta \right)+\tan 1° \tan 10° \tan 20° \tan 70° \tan 80° \tan 89°+\sec \left(90°-\theta \right).\mathrm{cosec} \theta -\tan \left(90°-\theta \right).\cot \theta$

If $\frac{\cos \alpha }{\cos \beta }=m \mathrm{and} \frac{\cos \alpha }{\sin \beta }=n$ then show that $\left(m^2+n^2\right) {\cos }^2\beta =n^2$

If $\tan A=\sqrt{2}-1.$ Show that $\sin A \cos A=\frac{\sqrt{2}}{4}.$

If $\sec \theta -\tan \theta =4$ then prove that $\cos \theta =\frac{8}{17}$.

Find the value of ${\sin }^{2}5°+{\sin }^{2}10°+{\sin }^{2}80°+{\sin }^{2}85°$.

If $a \sin \theta +b \cos \theta =c$, then prove that $a \cos \theta -b \sin \theta =\pm \sqrt{a^2+b^2-c^2}$.

Show that $\frac{\sin \theta -2 {\sin }^3\theta }{2 {\cos }^3\theta -\cos \theta }=\tan \theta$

Prove that $\frac{\tan \theta +\sec \theta -1}{\tan \theta -\sec \theta +1}=\frac{1+\sin \theta }{\cos \theta }$