Question

Hello can u please solve:if tan theta=1/root2,find the value of sin theta cos theta. ?

Answer 1

Given  : tan θ = 1/√2

To Find : Sinθ  and cosθ     or SinθCosθ

Solution:

tan θ = 1/√2

 Sec² θ = 1 + tan²θ

=>   Sec² θ = 1 +(1/√2)²

=> Sec² θ = 1 + 1/2

=> Sec² θ = 3/2

=> Cos² θ = 2/3   (Sec  θ  = 1/Cos  θ)

SinθCosθ

= Cosθ tan θ Cosθ

= Cos² θ  tan θ

= (2/3)(1/√2 )

= (√2)/3

SinθCosθ  = (√2)/3

Cos² θ = 2/3

=> Cos θ =± √2/√3

Sinθ = Cosθ tan θ  = (±√2/3 )(  1/√2 )

Sinθ =    ±1/√3

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