Advertisements
Advertisements
प्रश्न
If tanα = `m/(m + 1)`, tanβ = `1/(2m + 1)`, then α + β is equal to ______.
पर्याय
`pi/2`
`pi/3`
`pi/6`
`pi/4`
उत्तर
If tanα = `m/(m + 1)`, tanβ = `1/(2m + 1)`, then α + β is equal to `bbunderline(pi/4)`.
Explanation:
Given that tanα = `m/(m + 1)`, tanβ = `1/(2m + 1)`
tan(α + β) = `(tanalpha + tanbeta)/(1 - tanalpha tanbeta)`
= `(m/(m + 1) + 1/(2m + 1))/(1 - m/(m + 1) xx 1/(2m + 1))`
= `((2m^2 + m + m + 1)/((m + 1)(2m + 1)))/(((m + 1)(2m + 1) - m)/((m + 1)(2m + 1))`
= `(2m^2 + 2m + 1)/(2m^2 + 2m + m + 1 - m)`
= `(2m^2 + 2m + 1)/(2m^2 + 2m + 1)`
= 1
⇒ tan(α + β) = `tan pi/4`
∴ α + β = `pi/4`
APPEARS IN
संबंधित प्रश्न
Prove the following: `cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 - x)sin (pi/4 - y) = sin (x + y)`
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Prove the following:
sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x
Prove the following:
cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1
Prove the following:
cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
Prove that: `(cos x + cos y)^2 + (sin x - sin y )^2 = 4 cos^2 (x + y)/2`
Prove that: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2 (x - y)/2`
Evaluate the following:
cos 80° cos 20° + sin 80° sin 20°
Prove that:
\[\frac{7\pi}{12} + \cos\frac{\pi}{12} = \sin\frac{5\pi}{12} - \sin\frac{\pi}{12}\]
Prove that
Prove that \[\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1\].
Prove that:
sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.
If sin (α + β) = 1 and sin (α − β) \[= \frac{1}{2}\], where 0 ≤ α, \[\beta \leq \frac{\pi}{2}\], then find the values of tan (α + 2β) and tan (2α + β).
If sin α + sin β = a and cos α + cos β = b, show that
If sin α + sin β = a and cos α + cos β = b, show that
Prove that:
If \[\tan\theta = \frac{\sin\alpha - \cos\alpha}{\sin\alpha + \cos\alpha}\] , then show that \[\sin\alpha + \cos\alpha = \sqrt{2}\cos\theta\].
If 12 sin x − 9sin2 x attains its maximum value at x = α, then write the value of sin α.
Write the interval in which the value of 5 cos x + 3 cos \[\left( x + \frac{\pi}{3} \right) + 3\] lies.
If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B.
If tan (π/4 + x) + tan (π/4 − x) = a, then tan2 (π/4 + x) + tan2 (π/4 − x) =
Express the following as the sum or difference of sines and cosines:
2 sin 4x sin 3x
If 3 tan (θ – 15°) = tan (θ + 15°), 0° < θ < 90°, then θ = ______.
If sinθ + cosθ = 1, then find the general value of θ.
If sinθ + cosecθ = 2, then sin2θ + cosec2θ is equal to ______.
The value of tan 75° - cot 75° is equal to ______.
The value of sin(45° + θ) - cos(45° - θ) is ______.
State whether the statement is True or False? Also give justification.
If tan(π cosθ) = cot(π sinθ), then `cos(theta - pi/4) = +- 1/(2sqrt(2))`.
