If cos x = | sin x | then, the general solution is

x = ( 2 n + 1 ) π ± π 4 , n ∈ Z

x = n π + ( - 1 ) n π 4 , n ∈ Z

EASY

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Important Questions on Trigonometric Functions

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

tanx + tany = \frac{5}{6}

and

cotx + coty = 5

, then

\tan (x + y)

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

\sec^{4} θ - \sec^{2} θ = 3

the value of

\tan^{4} θ + \tan^{2} θ

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

\sec 4 θ = cosec (θ + 20^{o})

, then

θ

is equal to:

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

Which is the National Aquatic Animal of India?

HARD

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The number of principal solutions of

\tan 2 θ = 1

is:

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The value of

θ

with

0 \leq θ \leq 90 °

and

\sin^{2} θ + 2 \cos^{2} θ = \frac{7}{4}

is equal to

HARD

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

\cos x = | \sin x |

then, the general solution is

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The value of

\sin (45 ° + θ) - \cos (45 ° - θ)

is equal to

HARD

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

If sum of all the solutions of the equation

8 \cos x \cdot (\cos (\frac{π}{6} + x) \cdot \cos (\frac{π}{6} - x) - \frac{1}{2}) = 1

[0, π]

k π

, then

k

is equal to:

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

\sin φ - \cos φ = 0,

then the value of

\sin^{4} ϕ + \cos^{4} ϕ + \tan^{2} ϕ

is:

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The values of

x

0 \leq x \leq π

such that

\cos 2 x = cosx

are

HARD

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

One of the solutions of the equation

8 \sin^{3} θ - 7 + \sin θ + \sqrt{3} \cos θ = 0

lies in the interval

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The value of

\sin^{2} 1 ° + \sin^{2} 2 ° + \sin^{2} 3 ° + \dots + \sin^{2} 88 ° + \sin^{2} 89 °

is equal to

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The value of

\sin^{4} \frac{π}{8} + \sin^{4} \frac{3 π}{8}

is equal to

MEDIUM

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

\frac{\sin 91 ° + \sin 1 °}{\sin 91 ° - \sin 1 °} =

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The number of real numbers

λ

for which the equality

\frac{\sin (λ α)}{\sin α} - \frac{\cos (λ α)}{\cos α} = λ - 1

, holds for all real

α

which are not integral multiple of

π / 2

HARD

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The general solution of

\sin x - 3 \sin 2 x + \sin 3 x = \cos x - 3 \cos 2 x + \cos 3 x

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

\sin A + \sin^{2} A = 1,

then find the values of

\cos^{2} A + \cos^{4} A .

EASY

Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

The general solution of

\sqrt{3} \cos x + \sin x = \sqrt{2},

for an integer

n

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Mathematics>Trigonometry>Trigonometric Functions>Trigonometric Equations and the Solution

Which of the following is not a defining feature of all living organisms?

Energy is utilized by cells for

Important Questions on Trigonometric Functions

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