Question

If sin+ cos=7/5 then sin. Cos=
​

Answer 1

Step-by-step explanation:

GIVEN:

sin + cos= 7/5

Squaring on both sides

(sin + cos)² = 49/25

sin² + 2 sin.cos + cos² = 49/25

1 + 2sin.cos = 49/25........... ( sin² + cos²= 1)

2sin.cos = 49/25 - 1

2sin.cos = 24/25

so, sin.cos = 12/25

Answer 2

Given :-

$\sf \bigg( sin\theta + cos \theta \bigg) = \dfrac{7}{5}$

To find:-

• We have to find the value of

$\bullet\sf ( sin\theta) (cos \theta)$

• Identity used -

$\boxed{\sf\ (a+b)^2= a^2+b^2+2ab}$

$\underline{\bigstar{\sf\ sin^2\theta+cos^2\theta=1 }}$

Solution:-

$\dashrightarrow\sf (sin\theta+cos\theta)^2= sin^2\theta+cos^2\theta+2(sin\theta)(cos\theta)\\ \\ \\ \sf \bullet ( sin\theta+cos\theta)= \dfrac{7}{5}\\ \\ \\ \dashrightarrow\sf \bigg(\dfrac{7}{5}\bigg)^2= 1+2(sin\theta)(cos\theta)\\ \\ \\ \dashrightarrow\sf \dfrac{49}{25}-1= 2(sin\theta)(cos\theta)\\ \\ \\ \dashrightarrow\sf \bigg( \dfrac{49-25}{25}\bigg)= 2(sin\theta)(cos\theta)\\ \\ \\ \dashrightarrow\sf \bigg(\dfrac{\cancel{24}}{25\times \cancel{2}}\bigg)= (sin\theta)(cos\theta)\\ \\ \\ \dashrightarrow\sf \dfrac{12}{25}= (sin \theta)(cos\theta)$

$\boxed{\sf\ (sin\theta)(cos\theta)=\dfrac{12}{25}}$