Question

tanA + cot2A = cosec2A

Answer 1

Step-by-step explanation:

Let us consider the left hand side of equation,

LHS = cot2A + tanA

As we know,

cot2A=cos2A/sin2A and

tanA=sinA/cosA therefore,

LHS = (cos2A/sin2A)+(sinA/cosA)

LHS =(cos2A ×cosA + sin2A × sinA)/(sin2A × cosA)

…( cross multiplication)

We know the formula,

cos(2A - A) = cos2A × cos A + sin2A × sinA

So,

LHS = cos(2A - A) / (sin2A × cosA)

LHS = cosA / ( sin2A × cosA)

LHS = 1 / sin2A

LHS = cosec2A

LHS = RHS

therefore, tanA + cot2A = cosec2A

Hence proved