Question

(1 + tan 0)² + (1 + cot0)² = (sec0 + cosec0)?
prove it​

Answer 1

(1+tanθ)²+(1+cotθ)²=(1+(sinθ/cosθ))²+(1+(cosθ/sinθ))²

=(cosθ+sinθ)²/(cosθ)²+(sinθ+cosθ)²/(sinθ)²

=(1+2sinθcosθ)((1/cosθ)²+(1/sinθ)²)

=(1+2sinθcosθ)(1/((cosθ)²(sinθ)²)

=(1+2sinθcosθ)/((cosθ)²(sinθ)²)

=(secθ)²(cosecθ)²+2(secθ)(cosecθ)

=[secθcosecθ][secθcosecθ+2]

at θ=0

LHS=∞

and

RHS=∞

LHS=RHS

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