Advertisements
Advertisements
प्रश्न
Find the value of the expression `sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2))`
Advertisements
उत्तर
`sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2))`
⇒ `sin[tan^-1 ((2 xx 1/3)/(1 - (1/3)^2))] + cos[cos^-1 1/sqrt(1 + (2sqrt(2))^2)]` ......`[because tan^-1x = cos^-1 (1/sqrt(1 + x^2))]`
⇒ `sin[tan^-1 ((2/3)/(1 - 1/9))] + cos[cos^-1 (1/3)]`
⇒ `sin[tan^-1 (3/4)] + 1/3`
⇒ `sin[sin^-1 (3/5)] + 1/3`
⇒ `3/5 + 1/3`
⇒ `14/15` ......`[because tan^-1x = sin^-1 x/sqrt(1 + x^2)]`
Hence, `sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2)) = 14/15`
APPEARS IN
संबंधित प्रश्न
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
Find the principal value of the following:
`sin^-1(tan (5pi)/4)`
For the principal value, evaluate of the following:
`sin^-1(-1/2)+2cos^-1(-sqrt3/2)`
For the principal value, evaluate of the following:
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
Find the principal value of the following:
`tan^-1(-1/sqrt3)`
Find the principal value of the following:
`sec^-1(-sqrt2)`
Find the principal value of the following:
`sec^-1(2tan (3pi)/4)`
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
Find the value of `sec(tan^-1 y/2)`
Find the value of `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
Which of the following corresponds to the principal value branch of tan–1?
The principal value of the expression cos–1[cos (– 680°)] is ______.
The value of sin (2 sin–1 (.6)) is ______.
The value of the expression sin [cot–1 (cos (tan–11))] is ______.
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
Which of the following is the principal value branch of cos–1x?
The domain of the function cos–1(2x – 1) is ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
The principal value of `cos^-1 (- 1/2)` is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The value of `cos^-1 (cos (14pi)/3)` is ______.
The value of cos (sin–1x + cos–1x), |x| ≤ 1 is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The value of the expression (cos–1x)2 is equal to sec2x.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
What is the value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`
