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Trigonometric Ratios of Multiples of an Angle

Assertion-Rea...

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Assertion-Reasons: A: f(x)= sin^-1x+cos^-1x+2, d(f(x))/dx=0 R: d(sinx)/dx=cos x

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Q. Assertion :Statement 1 Range of

f (x) = {tan}^{- 1} x + {sin}^{- 1} x + {cos}^{- 1} x

(0, π)

Reason: Statement 2

f (x) = {tan}^{- 1} x + {sin}^{- 1} x + {cos}^{- 1} x = \frac{π}{2} + {tan}^{- 1} x

x ϵ (- 1, 1]

Q. Assertion (A) : The maximum value of

f (x) = {sin}^{- 1} x + {cos}^{- 1} x + {tan}^{- 1} x

\frac{3 π}{4}

{sin}^{- 1} x > {cos}^{- 1} x

x

R

c o s^{- 1} x = 2 s i n^{- 1} \sqrt{\frac{1 - x}{2}} = 2 c o s^{- 1} \sqrt{\frac{1 + x}{2}}

s i n^{- 1} (- x) = - s i n^{- 1} x, c o s^{- 1} (- x) = π - c o s^{- 1} x (- 1 \leq x \leq 1)

{cosec}^{- 1} (3 / 2) + {cos}^{- 1} (2 / 3) - 2 {cot}^{- 1} (1 / 7) - {cot}^{- 1} 7

{cot}^{- 1} 7

{sin}^{- 1} x + {cos}^{- 1} x = π / 2, {tan}^{- 1} x + {cot}^{- 1} x = π / 2, {cosec}^{- 1} x = {sin}^{- 1} (1 / x),

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

(s i n^{- 1} x + c o s^{- 1} x), x \in [- 1, 1] t h e n \frac{d y}{d x}

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Trigonometric Ratios of Multiples of an Angle

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