Question

Prove that: (sinθ+cosecθ)2+ (cosθ+secθ)2= 7+tan2θ+cot2θ .

Answer 1

Step-by-step explanation:

= ( sin2A+ 2.sinA.cosecA + cosec2A) + ( cos2A + 2.cosA.secA + sec2)

= sin2A + cos2A + cosec2A + sec2A + 2.sinA .cosecA + 2.cosA.secA

= 1+ ( 1+ cot2A ) + (1+ tan2A ) + 2.1 + 2.1

= 1+(1+cot2A) + (1+ tan2A ) +2+2

= 1+1+1+2+2+cot2A + tan2A

= 7+ cot2A + tan2A

= R.H.S

hence proved..