Advertisements
Advertisements
Question
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
Options
110
191
80
194
Advertisements
Solution
194
We have:
\[\tan A + \cot A = 4\]
Squaring both the sides:
\[ \left( \tan A + \cot A \right)^2 = 4^2 \]
\[ \Rightarrow \tan^2 A + \cot^2 A + 2 \left( \tan A \right)\left( \cot A \right) = 16\]
\[ \Rightarrow \tan^2 A + \cot^2 A + 2 = 16\]
\[ \Rightarrow \tan^2 A + \cot^2 A = 14\]
Squaring both the sides again:
\[ \left( \tan^2 A + \cot^2 A \right)^2 = {14}^2 \]
\[ \Rightarrow \tan^4 A + \cot^4 A + 2 \left( \tan^2 A \right)\left( \cot^2 A \right) = 196\]
\[ \Rightarrow \tan^4 A + \cot^4 A + 2 = 196\]
\[ \Rightarrow \tan^4 A + \cot^4 A = 194\]
APPEARS IN
RELATED QUESTIONS
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the general solution of cosec x = –2
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
In a ∆ABC, prove that:
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
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
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
If tan θ + sec θ =ex, then cos θ equals
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
The smallest positive angle which satisfies the equation
If \[4 \sin^2 x = 1\], then the values of x are
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
The number of values of x in the interval [0, 5 π] satisfying the equation \[3 \sin^2 x - 7 \sin x + 2 = 0\] is
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Solve the following equations:
sin 5x − sin x = cos 3
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
