Advertisements
Advertisements
Question
Find the value of the expression in terms of x, with the help of a reference triangle
cos (tan–1 (3x – 1))
Advertisements
Solution
cos (tan–1 (3x – 1)) = `cos["opp"/"Hyp"]`
Let θ = tan–1(3x – 1)
tan θ = 3x – 1
1 + tan2θ = 1 + (3x – 1)²
sec2θ = 9x2 – 6x + 2
sec θ = `sqrt(9x^2- 6x + 2)`
cos θ = `1/sqrt(9x^2 - 6x + 2)`
⇒ cos (tan–1(3x – 1)) = `1/sqrt(9x^2 - 6x + 2)`
APPEARS IN
RELATED QUESTIONS
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
Solve for x : tan-1 (x - 1) + tan-1x + tan-1 (x + 1) = tan-1 3x
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
`cos^(-1) (cos (7pi)/6)` is equal to ______.
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
Find the value of the expression in terms of x, with the help of a reference triangle
`tan(sin^-1(x + 1/2))`
Prove that `tan^-1x + tan^-1y + tan^-1z = tan^-1[(x + y + z - xyz)/(1 - xy - yz - zx)]`
The value of the expression `tan (1/2 cos^-1 2/sqrt(5))` is ______.
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
The value of cot–1(–x) for all x ∈ R in terms of cot–1x is ______.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"tan"^-1 (sqrt3)`
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:
𝐴' Is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA'B is ______.
`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
