37. cosec theta - sin theta = a cube sec theta - cos theta = b cube Prove that (a sq. * b sq.) [a sq. + b sq.] = 1

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(a) Prove that $\frac{c o s A}{1 + s i n A} + t a n A = s e c A$

(b) Prove the identity $(s i n θ + c o s θ) (t a n θ + c o t θ) = s e c θ + c o s e c θ$ [6 MARKS]

Q. If

a s i n θ + b c o s θ = a c o s e c θ - b s e c θ = 1,

prove that

a^{2} + b^{2} = 1 + b^{2 / 3} - b^{4 / 3}

Q. If

c o s e c θ - sin θ = a^{3}

and

sec θ - cos θ = b^{3}

, prove that

a^{2} b^{2} (a^{2} + b^{2}) = 1

Q. Prove the following trigonometric identities.

If cosec θ − sin θ = a³, sec θ − cos θ = b³, prove that a² b² (a² + b²) = 1

Q. Prove that :

{(s i n θ + s e c θ)}^{2} + {(c o s θ + c o s e c θ)}^{2} = {(1 + s e c θ c o s e c θ)}^{2}

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