Question

if sin theta +cos theta=1/√2 then find the value of 4sin theta cos theta
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Answer 1

Answer:

is 1 the answer is one hope it is useful

Answer 2

Step-by-step explanation:

Given :-

Sin θ + Cos θ = 1/√2

To find :-

Find the value of 4 Sin θ Cos θ ?

Solution :-

Given that :

Sin θ + Cos θ = 1/√2 -------------------(1)

On squaring both sides then

=> (Sin θ + Cos θ)² = (1/√2)²

=> Sin² θ + 2 Sin θ Cos θ + Cos² θ = 1/2

Since (a+b)² = a²+2ab+b²

Where a = Sin θ , b = Cos θ

=> (Sin² θ + Cos² θ) + 2 Sin θ Cos θ = 1/2

We know that Sin² A + Cos² A = 1

=> 1 + 2 Sin θ Cos θ = 1/2

=> 2 Sin θ Cos θ = (1/2) - 1

=> 2 Sin θ Cos θ = (1-2)/2

=> 2 Sin θ Cos θ = -1/2

On multiplying with 2 both sides then

=> 2 × 2 Sin θ Cos θ = -1/2 × 2

=> 4 Sin θ Cos θ = -2/2

=> 4 Sin θ Cos θ = -1

Answer:-

The value of 4 Sin θ Cos θ for the given problem is -1

Used formulae:-

• (a+b)² = a²+2ab+b²

• Sin² A + Cos² A = 1