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Trigonometric Ratios of Half Angles

10. If acose ...

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10. If acose + bsine = 3 and asine - bcos0 = 4, then a^2 b^2 has the value

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Q. If x = a sin θ + b cos 0 and y = a cos 0 b sin θ, prove that

x^{2} + y^{2} = a^{2} + b^{2} .

c o s θ + b s i n θ = 3

a s i n θ - b c o s θ = 4

a^{2} + b^{2}

has the value =

a c o s θ + b s i n θ = 4

a s i n θ - b c o s θ = 3

then, find the value of

a^{2} + b^{2}

x = \sqrt{a^{s i n^{- 1} t}}

y = \sqrt{a^{c o s^{- 1} t}}

, then the value of

\frac{d y}{d x}

x = a s i n

θ

+ b c o s

θ

y = a c o s

θ

- b s i n

θ

(a x + a y)^{2}

(b x - a y)^{2}

(a^{2} + b^{2})^{2}

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