Advertisements
Advertisements
प्रश्न
Prove the following:
`tan(pi/4 + theta) = (1 + tan theta)/(1 - tan theta)`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Prove the following:
`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`
Prove the following:
`sqrt(2)cos (pi/4 - "A")` = cos A + sin A
Prove the following:
`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find cos (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 `costheta/(1 + sin theta)` is equal to .....
Prove the following:
tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
`(sin8A + sin2A)/(cos2A - cos8A)` is equal to ______
If ABCD is a cyclic quadrilateral, then cos A + cos B + cos C + cos D = ______.
`(sec8A - 1)/(sec4A - 1)` = ______
If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.
If sin A + cos A = `sqrt(2)`, then the value of cos2 A is ______.
If `0 < β < α < π/4, cos (α + β) = 3/5` and cos (α – β) = `4/5`, then sin 2α is equal to ______.
If cos(81° + θ) = `sin(k/3 - θ)`, then k 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 ______.
If cos(A – B) = `3/5` and tan A tan B = 2, then ______.
tan 100° + tan 125° + tan 100° tan 125° = ______.
If `π/2 < α < π, π < β < (3π)/2`; sin α = `15/17` and tan β = `12/5`, then the value of sin(β – α) is ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
sin 4θ can be written as ______.
cos2 76° + cos2 16° – cos 76° cos 16° is equal to ______.
The value of cot 70° + 4 cos 70° is ______.
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
The value of tan 3A – tan 2A – tan A is ______.
