Question

If sin theta - cos theta = 0; show that sec theta = root2

Answer 1

$\sf\small\purple{Your Answer :-}$

Sinθ+Cosθ=√2

Or, (Sinθ+Cosθ)²=(√2)² [ By square both sides]

Or, Sin² + Cos² + 2 Sinθ Cosθ = 2

Or, 1+ 2 Sinθ. Cosθ = 2 [ as, Sin² + Cos² = 1]

Or, 2 Sinθ Cosθ = 2—1

Or, Sin 2θ = 1 [as, Sin 2θ = 2 Sinθ Cosθ ]

Or, Sin 2θ = Sin 90° [ as the value of Sin 90°= 1]

Or, 2θ = 90° [ Dividing Sin from both sides ]

Or, θ = 90°÷ 2 = 45°

So the value of θ is 45°.

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