sec 70° sin 20° – cos 20° cosec 70° = 0

(i) sec 70° sin 20° – cos 20° cosec 70° = 0

(ii) sin² 20° + sin² 70° – tan² 45° = 0.

Answer :

(i) sec 70° sin 20° – cos 20° cosec 70° = 0

LHS = sec 70° sin 20° – cos 20° cosec 70°

= sin 20°/cos 70° – cos 20°/sin 70°

= sin 20°/cos (90° – 20°) – cos 20°/sin (90° – 20°)

= sin 20°/sin 20° – cos 20°/cos 20°

= 1 – 1

= 0

= RHS

(ii) sin² 20° + sin² 70° – tan² 45° = 0

LHS = sin² 20° + sin² 70° – tan² 45°

= sin² 20° + sin² (90° – 20°) – tan² 45°

= sin² 20° + cos² 20° – tan² 45°

sin² θ + cos² θ = 1 and tan 45° = 1

= 1 – 1

= 0

= RHS

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