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:
sin [(n + 1)A]. sin [(n + 2)A] + cos [(n + 1)A]. cos [(n + 2)A] = cos A
Prove the following:
`(cos(x - y))/(cos(x + y)) = (cotx coty + 1)/(cotx coty - 1)`
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find sin (A + B)
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
Select the correct option from the given alternatives :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
Select the correct option from the given alternatives:
The value of `costheta/(1 + sin theta)` is equal to .....
Select the correct option from the given alternatives :
The numerical value of tan 20° tan 80° cot 50° is equal to ______.
Prove the following:
tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
The value of sin 163° cos 347° + sin 167° sin 73° is ______
In Δ ABC, if tan A + tan B + tan C = 6 and tan A tan B = 2 then tan C = ______.
`(tanA + secA - 1)/(tanA - secA + 1)` = ______
`(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 `α, β ∈ (0, π/2)`, sin α = `4/5` and cos (α + β) = `-12/13`, then sin β is equal to ______.
If A + B = 45°, then (cot A – 1) (cot B – 1) 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 ______.
If tan α, tan β are the roots of the equation x2 + px + q = 0 (p ≠ 0), then ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
If cos 2B = `(cos(A + C))/(cos(A - C))`, then tan A, tan B, tan C are in ______.
The value of cot 70° + 4 cos 70° is ______.
If A, B, C, D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to ______.
cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
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 ______.
