Question

sin thita + cos thita = 2, than sin thita × cos thita=?​

Answer 1

Answer- The above question is from the chapter 'Trigonometric Identities'.

Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.

Trigonometric Ratios:

sin θ  = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ

Trigonometric Identities:

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

Concept used: i) (a + b)² = a² + b² + 2ab

ii) sin²θ + cos²θ = 1

Given question: sin θ + cos θ = 2, then sin θ × cos θ = ___ .

Solution: It is given that sin θ + cos θ = 2.

Squaring both sides we get,

(sin θ + cos θ)² = 2²

[Applying identity: (a + b)² = a² + b² + 2ab where a = sin θ and b = cos θ]

sin²θ + cos²θ + 2 sinθ cosθ = 4

1 + 2 sinθ cosθ = 4 ( ∵ sin²θ + cos²θ = 1)

2 sinθ cosθ = 4 - 1

2 sinθ cosθ = 3

sinθ cosθ = $\frac{3}{2}$

∴ The value of sin θ × cos θ = $\frac{3}{2}$ .