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