#### (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°

sin^{2} θ + cos^{2} θ = 1

= sin^{2} 63° + cos^{2} 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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