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Range of Trigonometric Ratios from 0 to 90 Degrees

If x (0,/2) ...

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If x (0,/2) prove that sin(cosx) < cos (sinx)

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Q. Prove that cosecx(secx -1) - cot x(1- cosx) = sinx-sinxcosx

{s i n}^{3} x + {c o s}^{3} x = (s i n x + c o s x) (1 - s i n x c o s x)

sin x = 3 cos x

sin x cos x

s i n x + s i n y = 2 s i n \frac{x + y}{2} c o s \frac{x - y}{2}

and hence show that

\frac{s i n x + s i n 3 x}{c o s x + c o s 3 x} = t a n 2 x

f (x) = sin x + sin x cos \frac{x}{2} + sin x {cos}^{2} \frac{x}{2} + . . . .

g (x) = f (x) . sin \frac{x}{4} - cos \frac{x}{4}

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Range of Trigonometric Ratios from 0 to 90 Degrees

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