Question

Prove:-

Cot²θ (secθ -1)/(1+sinθ ) + sec²θ (sinθ -1) / ( 1+secθ ) = 0

━━━━━━━━━━━━━

Plz Give Answer in detail.....
Don't spam!!​

Answer 1

Solution

Take LHS

Cot²θ(secθ-1)/(1+sinθ)+ sec²θ(sinθ-1)/(1+secθ)

= cot²θ(secθ-1)(1+secθ)+sec²θ(sinθ-1)(1+sinθ) / (1+sinθ)(1+secθ)

= cot²θ(sec²-1)+sec²θ(sin ²-1) / (1+sin θ)(1+secθ)

= cot²θ tan ²θ+ sec²θ(-cos²θ)/ (1+sin θ) ( 1+sec θ)

= cot ²θ + tan²θ- sec²θcos²θ/ ( 1+ sin θ) ( 1+ sec θ)

= cot²θ×1/cot²θ - sec²θ×1/sec²θ / ( 1+sin θ) ( 1+ secθ)

= 1/(1+sin θ)(1+ secθ)

Hence proveed !!!