LHS =

= sin 9° ×  sin 27° = sin(90° - 81°)  sin(90° - 63°)

=  cos 63° × cos 81° = RHS

$$\therefore$$ LHS = RHS proved.

Soln

LHS = sin1°. sin2°. sin45° .sec88° .sec89° = 1

= sin1°.sin2°.1.sec(90° - 2°).sec(90° - 1°)

= sin1°.sin2°.1.cosec2°.cosec1°

= sin1°.cosec1°.sin2°.cosec2°

= 1×1

= 1 = RHS

$$\therefore$$ LHS = RHS

LHS = sec$$\theta$$.cosec$$\theta$$(90° - $$\theta$$) - tan$$\theta$$.cot(90° - $$\theta$$) = 1

= sec$$\theta$$.sec$$\theta$$ - tan$$\theta$$.tan$$\theta$$

= sec2$$\theta$$ - tan2$$\theta$$

= 1

= 1 = RHS

$$\therefore$$ LHS = RHS proved.

Soln

LHS = $$\frac{cos(90°+θ).sec(-θ).tan(180° - θ)}{sec(360° + θ).sin(180°+θ).cot(90°-θ)}$$ = -1

= $$\frac{cos(90°+θ).sec(-θ).tan(180° - θ)}{sec(4×90° + θ).sin(2×90°+θ).cot(90°-θ)}$$

= $$\frac{-sinθ.secθ(-tanθ)}{secθ(-sinθ).tanθ}$$

= -1 = RHS

$$\therefore$$ LHS = RHS proved.

Soln

LHS = sin70°.cos20° + sin20°.cos70°

= sin70°.cos(90° - 70°) + sin(90° - 70°).cos70°

= sin70°. sin70° + cos70°.cos70°

= sin270° + cos270° = 1