Advertisements
Advertisements
प्रश्न
Write the value of sin−1 (sin 1550°).
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
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
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)=cos^-1x+cosx.`
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
`sin(sin^-1 1/5+cos^-1x)=1`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Solve the following equation for x:
`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
Write the principal value of `sin^-1(-1/2)`
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
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 =
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is
If \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
The period of the function f(x) = tan3x is ____________.
