Question

prove that tan theta + cot theta the whole square is equal to sec square theta plus cosec square
​

Answer 1

Answer:

the required proof is in the above image

Answer 2

Answer:

(tanθ + Cotθ)² = Sec²θ + Cosec²θ

Step-by-step explanation:

(tanθ + Cotθ)² = Sec²θ + Cosec²θ

LHS

= (tanθ + Cotθ)²

= (Sinθ/Cosθ  + Cosθ/Sinθ)²

= (( Sin²θ + Cos²θ)/CosθSinθ )²

= 1/Cos²θSin²θ

RHS

= Sec²θ + Cosec²θ

= 1/Cos²θ  + 1/Sin²θ

= (Sin²θ + Cos²θ)/(Cos²θSin²θ)

= 1/Cos²θSin²θ

LHS = RHS

QED

Proved

(tanθ + Cotθ)² = Sec²θ + Cosec²θ