Advertisements
Advertisements
Question
Find the principal value of the following:
`sec^-1 (-sqrt2)`
Advertisements
Solution
Let `sec^-1 (-sqrt2)` = y
`-sqrt2` = sec y
sec y = `- sqrt2`
`1/(cos y) = - sqrt2`
Taking reciprocal cos y = `((-1)/sqrt2)` [where 0 ≤ y ≤ π]
cos y = `cos (pi - pi/4) [cos pi/4 = 1/sqrt2 = cos (180^circ - theta) = - cos theta]`
`= cos ((4pi - pi)/4) = cos (3pi)/4`
∴ The principal value of sec-1 `(- sqrt2)` is `(3pi)/4`
APPEARS IN
RELATED QUESTIONS
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
Find the principal value of the following: tan-1(– 1)
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
Find the principal value of `tan^-1 (sqrt(3))`
In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
3 tan-1 a is equal to ____________.
If –1 ≤ x ≤ 1, the prove that sin–1 x + cos–1 x = `π/2`
