Question

Prove the following :

(i) sin θ sin (90° − θ) − cos θ cos (90° − θ) = 0
(ii) $\frac{\cos \left(90°-\theta \right)\sec \left(90°-\theta \right)\tan \theta }{\mathrm{cosec}\left(90°-\theta \right)\sin \left(90°-\theta \right)\cot \left(90°-\theta \right)}+\frac{\tan \left(90°-\theta \right)}{\cot \theta }=2$
(iii) $\frac{\tan \left(90°-A\right)\cot A}{{\mathrm{cosec}}^{2}A}-{\cos }^{2}A=0$
(iv) $\frac{\cos \left(90°-A\right)\sin \left(90°-A\right)}{\tan \left(90°-A\right)}={\sin }^{2}A$
(v) sin (50° − θ) − cos (40° − θ) + tan 1° tan 10° tan 20° tan 70° tan 80° tan 89° = 1

Answer 1

(i) We have to prove:

Left hand side

=Right hand side

Proved

(ii) We have to prove:

Left hand side

= right hand side

Proved

(iii) We have to prove:

Left hand side

= right hand side

Proved

(iv) We have to prove:

Left hand side

= Right hand side

Proved

(v) We have to prove:

Left hand side

Since .So

=Right hand side

Proved