sin 63° cos 27° + cos 63° sin 27° = 1

(i) sin 63° cos 27° + cos 63° sin 27° = 1

(ii) sec 31° sin 59° + cos 31° cosec 59° = 2.

Answer :

(i) sin 63° cos 27° + cos 63° sin 27° = 1

LHS = sin 63° cos 27° + cos 63° sin 27°

= sin 63° cos (90° – 63°) + cos 63° sin (90° – 63°)

= sin 63° sin 63° + cos 63° cos 63°

sin² θ + cos² θ = 1

= sin² 63° + cos² 63°

= 1

(ii) sec 31° sin 59° + cos 31° cosec 59° = 2

LHS = sec 31° sin 59° + cos 31° cosec 59°

= 1/cos 31° × sin 59° + (cos 31° × 1/sin 59°)

= sin 59°/cos (90° – 59°) + cos 31°/sin (90° – 31°)

= sin 59°/sin 59° + cos 31°/cos 31°

= 1 + 1

= 2

= RHS

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