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Range of Trigonometric Ratios from 0 to 90 Degrees

If [0, 1], th...

Question

If [0, 1], then sin–1x + cot–1x + cos–1x + tan–1x is equal to

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{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

{s i n}^{- 1} (1 - x) - 2 {s i n}^{- 1} x = π / 2

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f (x) = {tan}^{- 1} x - {cot}^{- 1} x,

g (x) = {sec}^{- 1} x - {cosec}^{- 1} x,

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x \geq 0

θ = {sin}^{- 1} x + {cos}^{- 1} x - {tan}^{- 1} x

{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

u = {c o t}^{- 1} [\sqrt{c o s 2 θ}] - {t a n}^{- 1} [\sqrt{c o s 2 θ}]

s i n u = {t a n}^{2} θ

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