Question

If a sin o + b cos o = a cosec o - b sec o =1, prove that a^2 + b^2 = 1 + b^2/3 - b^4/3.
(No silly answers please)

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Answer 1

Answer:

$asinθ+bcosθ=1</p><p></p><p>$

$acosθ−bsinθ=sinθ⋅cosθ</p><p></p><p>$

$a2+b2=1+sin2θcos2θ </p><p></p><p>$

$</p><p>=1+cos2θ−cos4θ</p><p></p><p>$

Now we have to get only b in L. H. S.

Multiply the given equation by cosθandsinθ and subtracting , we get

$b(cos2θ+sin2θ)=cosθ−cosθ⋅sin2θ</p><p></p><p>$

$or b = cos3θ∴cosθ=b1/3</p><p></p><p>$

$∴a2+b2=1+b2/3−b4/3</p><p></p><p>$