Question

If sec theta + tan theta is equal to m show that n square minus one by n square + 1 is equal to sin theta

Answer 1

Correct Question : If Sec θ + tan θ = m , Show that Sin θ = 2m² + 1 / m² + 1

Given : Sec θ + tan θ = m

Proof : Sec θ + tan θ = m

1/ Cos θ + Sin θ / Cos θ = m

1 + Sin θ / Cos θ = m

1 + Sin θ = m Cos θ ....(i)

Here, Squaring on both Sides i.e LHS and RHS of Equation ....(i)

(1 + Sin θ )² = m² Cos²θ

1 + Sin²θ + 2 Sin θ = m² Cos²θ

1 + 1 - Cos²θ + 2 Sin θ = m² Cos²θ

2 +2 Sin θ - Cos²θ = m² Cos²θ

2 ( 1 + Sin θ ) - Cos²θ = m² Cos²θ

2 ( m Cos θ ) - Cos²θ = m² Cos²θ

m² Cos²θ + Cos²θ = 2m Cos θ

Cos²θ ( m² + 1 ) = 2m Cos θ

Cosθ = 2m/m²+1

Now, Substitute the Value of Cos θ in Equation (1) ...

1 + Sin θ = m Cos θ ....(i)

1+ Sin θ = m × 2m/m²+1

1 + Sin θ = 2m² / m² + 1

Sin θ = (2m² / m² + 1 ) + (1/1)

Sin θ = 2m² + 1 / m² + 1

Proved

Answer 2

Your answer is in the attachment provided.

So please refer it .

And a Small correction in the question :-

If sec theta + tan theta is equal to m show that m square minus one by m square + 1 is equal to sin theta