Question

sinQ+cosQ=2 then what is sinQ*cosQ

Answer 1

Answer:

(3/2)

Step-by-step explanation:

= > sinQ + cosQ = 2

Square on both sides:

= > (sinQ + cosQ)² = 2²

= > (sinQ)² + (cosQ)² + 2sinQ.cosQ = 4

= > sin²Q + cos²Q + 2sinQ.cosQ = 4

sin²A + cos²A = 1

= > 1 + 2sinQ.cosQ = 4

= > 2sinQ.cosQ = 4 - 1 = 3

= > sinQ.cosQ = (3/2)

Answer 2

$\sin Q + \cos Q = 2$

Squaring both sides, we get,

${( \sin Q + \cos Q)}^{2} = 4$

$\implies \sin^{2}Q + \cos^{2} Q + 2 \sin Q \cos Q = 4$

$\implies 1 + 2 \sin(Q) \cos(Q) = 4$

$\implies2 \sin(Q) \cos(Q) = 3$

$\implies \sin(Q) \cos(Q) = \frac{3}{2}$