Advertisements
Advertisements
Question
Prove the following:
`tan(pi/4 + theta) = (1 + tan theta)/(1 - tan theta)`
Advertisements
Solution
`L.H.S. = tan(pi/4 + theta)`
According to `tan(A + B) = (tan A + tan B) / (1-tan A tan B`,
We get
`L.H.S. = (tan pi/4 + tan theta)/(1 - tan pi/4 tan theta)`
`L.H.S = (1 + tan theta)/(1 -(1) tan theta)` ...[because `tan pi/4 = 1]`
=`(1 + tan theta) / (1 - tan theta)`
Here `L.H.S = R.H.S`, Hence proved
Notes
APPEARS IN
RELATED QUESTIONS
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find tan (A + B)
If tan A = `5/6, tan "B" = 1/11`, prove that A + B = `pi/4`
Select the correct option from the given alternatives :
The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to
Prove the following:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
Prove the following:
tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
Prove the following:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.
The value of sin 163° cos 347° + sin 167° sin 73° is ______
`sqrt3 sin15^circ + cos15^circ` = ______
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
`(tanA + secA - 1)/(tanA - secA + 1)` = ______
If A, B, C are the angles of ΔABC, then `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2` = ______
`(sin8A + sin2A)/(cos2A - cos8A)` is equal to ______
`(sec8A - 1)/(sec4A - 1)` = ______
If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.
If equation tan θ + tan 2θ + tan θ tan 2θ = 1, θ = ______.
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
If cos (α + β) = `4/5` and sin (α – β) = `5/13`, where `0 ≤ α, β ≤ π/4`, then tan 2α is equal to ______.
If α + β = `π/2` and β + γ = α, then the value of tan α is ______.
lf sin θ = cos θ, then the value of 2 tan2 θ + sin2 θ – 1 is equal to ______.
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin 31^circ) - 8 sin^2 30^circ` is equal to ______.
If cos θ = `8/17` and θ lies in the 1st quadrant, then the value of cos(30° + θ) + cos(45° – θ) + cos(120° – θ) is ______.
The expression cos2(A – B) + cos2 B – 2 cos(A – B) cos A cos B is ______.
tan 100° + tan 125° + tan 100° tan 125° = ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
The value of `sin π/16 sin (3π)/16 sin (5π)/16 sin (7π)/16` is ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
