Advertisements
Advertisements
प्रश्न
If tanθ = `a/b`, then bcos2θ + asin2θ is equal to ______.
पर्याय
a
b
`a/b`
None
Advertisements
उत्तर
If tanθ = `a/b`, then bcos2θ + asin2θ is equal to b.
Explanation:
Given that: tanθ = `a/b`
bcos2θ + asin2θ = `b[(1 - tan^2 theta)/(1 + tan^2 theta)] + a[(2 tan theta)/(1 + tan^2 theta)]`
= `b[(1 - a^2/b^2)/(1 + a^2/b^2)] + a[((2a)/b)/(1 + a^2/b^2)]`
= `b[(b^2 - a^2)/(b^2 + a^2)] + [((2a^2)/b)/((b^2 + a^2)/b^2)]`
= `(b^3 - a^2b)/(b^2 + a^2) + (2a^2b)/(b^2 + a^2)`
= `(b^3 - a^2b + 2a^2b)/(b^2 + a^2)`
= `(b^3 + a^2b)/(b^2 + a^2)`
= `(b(b^2 + a^2))/(b^2 + a^2)`
= b
APPEARS IN
संबंधित प्रश्न
Prove that: `sin^2 pi/6 + cos^2 pi/3 - tan^2 pi/4 = -1/2`
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
Prove the following:
cos 4x = 1 – 8sin2 x cos2 x
Prove that: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2 (x - y)/2`
Prove that: sin 3x + sin 2x – sin x = 4sin x `cos x/2 cos (3x)/2`
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:
Prove that:
Prove that:
sin2 B = sin2 A + sin2 (A − B) − 2 sin A cos B sin (A − B)
If tan x + \[\tan \left( x + \frac{\pi}{3} \right) + \tan \left( x + \frac{2\pi}{3} \right) = 3\], then prove that \[\frac{3 \tan x - \tan^3 x}{1 - 3 \tan^2 x} = 1\].
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
Prove that:
If sin α sin β − cos α cos β + 1 = 0, prove that 1 + cot α tan β = 0.
Find the maximum and minimum values of each of the following trigonometrical expression:
sin x − cos x + 1
Reduce each of the following expressions to the sine and cosine of a single expression:
cos x − sin x
If α + β − γ = π and sin2 α +sin2 β − sin2 γ = λ sin α sin β cos γ, then write the value of λ.
If x cos θ = y cos \[\left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)\]then write the value of \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\]
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 sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β).
The value of \[\sin^2 \frac{5\pi}{12} - \sin^2 \frac{\pi}{12}\]
If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to
tan 20° + tan 40° + \[\sqrt{3}\] tan 20° tan 40° is equal to
If \[\tan A = \frac{a}{a + 1}\text{ and } \tan B = \frac{1}{2a + 1}\]
If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
The value of \[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\] is
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 cos 7x cos 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 tanA = `1/2`, tanB = `1/3`, then tan(2A + B) is equal to ______.
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.
State whether the statement is True or False? Also give justification.
If tanθ + tan2θ + `sqrt(3)` tanθ tan2θ = `sqrt(3)`, then θ = `("n"pi)/3 + pi/9`
