Advertisements
Advertisements
Question
Evaluate:
`cos(tan^-1 3/4)`
Advertisements
Solution
We have
`cos(tan^-1 3/4)=cos[1/2cos^-1((1-(3/4)^2)/(1+(3/4)^2))]` `[therefore 2tan^-1x+cos^-1((1-x^2)/(1+x^2))]`
`=cos[1/2cos^-1(7/25)]`
Let
`y=cos^-1(7/25)`
`=>cosy=7/25`
Now,
`cos[1/2cos^-1(7/25)]=cos[1/2y]`
`=sqrt((cosy+1)/2)` `[thereforecos2x=2cos^2x-1]`
`=sqrt((7/25+1)/2)`
`=sqrt(32/50)`
`=4/5`
`therefore cos[tan^-1(3/4)]=4/5`
APPEARS IN
RELATED QUESTIONS
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`cos^-1(cos3)`
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^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
If `cot(cos^-1 3/5+sin^-1x)=0`, find the values of x.
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
`4sin^-1x=pi-cos^-1x`
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
The number of real solutions of the equation \[\sqrt{1 + \cos 2x} = \sqrt{2} \sin^{- 1} (\sin x), - \pi \leq x \leq \pi\]
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Find the domain of `sec^(-1) x-tan^(-1)x`
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
