Advertisements
Advertisements
प्रश्न
Write the value of sin−1 (sin 1550°).
Advertisements
उत्तर
We know that
\[\sin^{- 1} \left( \sin{x} \right) = x\]
Now,
\[\sin^{- 1} \left( \sin {1550}^\circ \right) = \sin^{- 1} \left\{ \sin\left( {1620}^\circ - {1550}^\circ \right) \right\} \left[ \because \sin{x} = \sin\left( {1620}^\circ - x \right) \right]\]
\[ = \sin^{- 1} \left( \sin {70}^\circ \right)\]
\[ = {70}^\circ \]
\[\]
∴ \[\sin^{- 1} \left( \sin {1550}^\circ \right) = {70}^\circ\]
APPEARS IN
संबंधित प्रश्न
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the value of sin (cot−1 x).
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
