Question

sec A / tan A+cot A= sin A

Answer 1

LHS = sec A / tan A + cot A
= (1/cosA) / (sin A / cos A) + (cos A / sin A)
= (1/cos A)/sin^2 A + cos^2 A / sin A cos A
= 1/cos A / 1/sinAcosA
= sin A
= RHS

Answer 2

Question :

Prove that sec A / tan A+cot A= sin A

Answer :

The given equation is proved.

Given :

The equation sec A / tan A+cot A= sin A

To find :

To prove that the equation is true

Solution :

L.H.S

sec A / tan A + cot A

R.H.S

sin A

Solving L.H.S :

sec A/(tan A+ cot A)

= (1/cos A)/[(sin A/cos A) + (cos A/sin A)]

= (1/cos A)/[(sin^2 A + cos^2 A)/sin A cos A]

= (1/cos A)/[1/sin A cos A]

= (1/cos A)*(cos A*sin A)

= sin A

= R.H.S

Therefore , sec A / tan A+cot A= sin A (Hence Proved)

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