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`
Advertisements
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
Find the value of: tan 15°
Prove the following: `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`
Prove the following:
`cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`
Prove the following:
cos2 2x – cos2 6x = sin 4x sin 8x
Prove the following:
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Prove the following:
cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1
If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
cos (A − B)
If \[\cos A = - \frac{24}{25}\text{ and }\cos B = \frac{3}{5}\], where π < A < \[\frac{3\pi}{2}\text{ and }\frac{3\pi}{2}\]< B < 2π, find the following:
cos (A + B)
Evaluate the following:
sin 78° cos 18° − cos 78° sin 18°
If \[\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}\], where A lies in the second quadrant and B in the third quadrant, find the values of the following:
tan (A + B)
Prove that:
Prove that:
Prove that:
\[\frac{\sin \left( A - B \right)}{\cos A \cos B} + \frac{\sin \left( B - C \right)}{\cos B \cos C} + \frac{\sin \left( C - A \right)}{\cos C \cos A} = 0\]
If tan (A + B) = x and tan (A − B) = y, find the values of tan 2A and tan 2B.
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).
Prove that:
\[\frac{1}{\sin \left( x - a \right) \sin \left( x - b \right)} = \frac{\cot \left( x - a \right) - \cot \left( x - b \right)}{\sin \left( a - b \right)}\]
Prove that:
Find the maximum and minimum values of each of the following trigonometrical expression:
12 cos x + 5 sin x + 4
Find the maximum and minimum values of each of the following trigonometrical expression:
\[5 \cos x + 3 \sin \left( \frac{\pi}{6} - x \right) + 4\]
Reduce each of the following expressions to the sine and cosine of a single expression:
24 cos x + 7 sin x
Prove that \[\left( 2\sqrt{3} + 3 \right) \sin x + 2\sqrt{3} \cos x\] lies between \[- \left( 2\sqrt{3} + \sqrt{15} \right) \text{ and } \left( 2\sqrt{3} + \sqrt{15} \right)\]
tan 3A − tan 2A − tan A =
If tan 69° + tan 66° − tan 69° tan 66° = 2k, then k =
Express the following as the sum or difference of sines and cosines:
2 sin 3x cos x
Express the following as the sum or difference of sines and cosines:
2 cos 3x sin 2xa
If sinθ + cosθ = 1, then find the general value of θ.
If sinθ + cosecθ = 2, then sin2θ + cosec2θ is equal to ______.
If f(x) = cos2x + sec2x, then ______.
[Hint: A.M ≥ G.M.]
If tan θ = 3 and θ lies in third quadrant, then the value of sin θ ______.
The value of sin(45° + θ) - cos(45° - θ) is ______.
If tanA = `1/2`, tanB = `1/3`, then tan(2A + B) is equal to ______.
If sinx + cosx = a, then sin6x + cos6x = ______.
State whether the statement is True or False? Also give justification.
If tanA = `(1 - cos B)/sinB`, then tan2A = tanB
