Question

if cot theta =-3/4 and theta lies in the second quadrant , the. D Find the values of sin 2 Theta and cos 2 theta​

Answer 1

Answer is given in picture, it it is useful

Answer 2

Given :-

• cot θ = (-3/4)
• θ lies in 2nd quadrant .

To Find :-

• sin 2θ = ?
• cos 2θ = ?

Solution :-

we know that,

• In second quadrant , sin θ is positive only .
• cot θ = Base / perpendicular .
• sin θ = P / H
• cos θ = B / H
• H² = B² + P²

so ,

→ B / P = (3/4)

→ B = 3

→ P = 4

then,

→ H = √(B² + P²)

→ H = √(3² + 4²)

→ H = √(9 + 16)

→ H = √25 = 5

therefore,

→ sin 2θ = 2 * sin θ * cos θ

→ sin 2θ = 2 * (P / H) * (B / H)

→ sin 2θ = 2 * (4/5) * (-3/5)

→ sin 2θ = (-24/25) (Ans.)

and,

→ cos 2θ = 2cos²θ - 1

→ cos 2θ = 2(-3/5)² - 1

→ cos 2θ = 2(9/25) - 1

→ cos 2θ = (18/25) - 1

→ cos 2θ = (18 - 25)/25

→ cos 2θ = (-7/25) (Ans.)

Learn more :-

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tanA/(1-cotA) + cotA/(1-tanA)

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