Question

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If sinθ+cosθ=1, then (sinθ cosθ) is equal to?

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Answer 1

Answer:

$\sin(theta) + \cos(theta) = 1 \\ \\ \: it \: is \: given \: \\ so \: \: \: \\ see \: \\ the \: above \: \\ attachement \:$

Do the squaring on both sides.

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Answer 2

Step-by-step explanation:

Given :-

sinθ+cosθ=1

To find:-

Find the value of sinθ cosθ?

Solution:-

Given that :-

Sinθ + Cosθ = 1

On squaring both sides then

(Sinθ + Cosθ)^2 = (1)^2

=>(Sinθ + Cosθ )^2 = 1

LHS is in the form of (a+b)^2

Where a = Sinθ and b = Cosθ

We know that

(a+b)^2=a^2+2ab+b^2

=> Sin^2θ + 2 Sinθ Cosθ+ Cos^2θ = 1

=> ( Sin^2θ+Cos^2θ) + 2 Sinθ Cosθ = 1

We know that

Sin^2 A + Cos^2 A = 1

=> (1)+2 Sinθ Cosθ = 1

=> 1+ 2 Sinθ Cosθ = 1

=> 2 Sinθ Cosθ = 1-1

=> 2 Sinθ Cosθ = 0

=>Sinθ Cosθ = 0/2

=>Sinθ Cosθ = 0

Answer:-

The value of Sinθ Cosθ for the given problem is

0

Used formulae:-

• (a+b)^2=a^2+2ab+b^2

• Sin^2 A + Cos^2 A = 1