Question

if asintheta+bcostheta=c & acosectheta+bsectheta=c then prove that sin2theta=2ab/c^2-a^2-b^2

Answer 1

Answer:

ANSWER

Let θ be an angle such that

... a cos θ + b sin θ = c ............. (1)

Squaring both sides,

... a² cos² θ + b² sin² θ +2ab sin θ cos θ = c²

∴ a² ( 1 - sin² θ ) + b² ( 1 - cos² θ ) +2ab sin θ cos θ = c²

∴ a² - a² sin² θ + b² - b² cos² θ +2ab sin θ cos θ = c²

∴ a² + b² - c² = a² sin² θ + b² cos² θ - 2ab sin θ cos θ

∴ ( √(a²+b²-c²) )² = ( a sin θ - b cos θ )²

∴ a sin θ - b cos θ = ± √(a²+b²-c²)

Hence, Proved

Step-by-step explanation:

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