Question

if sin∅ + cos∅=√2 then sin∅*cos∅=?

Answer 1

$\huge\underline\mathfrak\white{Answer }$

$sin \alpha \times cos \alpha = \frac{1}{2}$

NOTE :- I have used alpha instead of theta.

Step - by - step explanation

Given

$sin \: \alpha \: + cos \: \alpha = \sqrt{2} \: \: \: .....(1)$

To find

$sin \: \alpha \times \: cos \: \alpha$

Solution

By squaring both sides in equation (1), we get,

${(sin \alpha + cos \alpha )}^{2} = {( \sqrt{2} )}^{2} \\ \\ {sin \alpha }^{2} + 2 \times sin \alpha \times cos \alpha + {cos \alpha }^{2} = 2 \: \: \: ..... {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \\ \: \: \: ...(2)$

Now,

By using the values in the equation (2), we get,

${sin \alpha }^{2} + {cos \alpha }^{2} + 2 \times sin \alpha \times cos \alpha = 2 \\ \\ 1 + 2 \times sin \alpha \times cos \alpha = 2 \: \: \: .....( {sin \alpha }^{2} + {cos \alpha }^{2} = 1) \\ 2 \times sin \alpha \times cos \alpha = 2 - 1 \\ 2 \times sin \alpha \times cos \alpha = 1 \\ \\ sin \alpha \times cos \alpha = \frac{1}{2}$

Ans.

$sin \alpha \times cos \alpha = \frac{1}{2}$

Hope it helps

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