Question

Solve this- (1-cot200°)(1-cot25°)

Answer 1

( 1 - cot 200°)( 1 - cot25°)

= ( sin200° - cos200°)( sin25° - cos25°)/( sin200°.sin25°

= ( sin200° + sin110°)( sin25° -sin65°)/sin200°.sin25°

= {2sin( 200+110)/2.cos(200-110)/2 }{ 2cos( 25 + 65)/2.(-sin( 65-25)/2)}/sin200.sin25°

= -4{ ( sin155°.cos45°)(cos45°.sin20°)/sin(180+20°).sin25°

= -4 × { sin45°× cos45°} sin( 180-25).sin20°./( -sin20°)(sin25°)

= 4 ×1/√ 2× 1/√2 sin25.sin20°/sin20.sin25°

= 4 × 1/2 = 2 ( answer )

Answer 2

( 1 - cot 200°)( 1 - cot25°)

= ( sin200° - cos200°)( sin25° -cos25°)/( sin200°sin25°)

= ( sin200° + sin110°)( sin25° -sin65°)/sin200°sin25°

= {2sin( 200+110)/2cos(200-110)/2 }{ 2cos( 25 + 65)/2(-sin( 65-25)/2)}/sin200°sin25°

= -4{(sin155°cos45°)(cos45°sin20°)/sin(180°+20°)sin25°

= -4{ sin45°×cos45°} sin( 180°-25°)sin20°/(-sin20°)(sin25°)

= 4×1/√2×1/√2 sin25°sin20°/sin20°sin25°

= 4×1/2=2