Advertisements
Advertisements
Question
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
Options
b2 − 1, if `"b" ≤ sqrt(2)`
b2 − 1, if `"b" > sqrt(2)`
b2 − 1, if b ≥ 1
b2 − 1, if `"b" ≥ sqrt(2)`
Solution
b2 − 1, if `"b" ≤ sqrt(2)`
APPEARS IN
RELATED QUESTIONS
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
Write the number of points of intersection of the curves
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x
