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

The solution of sin x = - 3 2 is

x = n π + - 1 n - π 3 , where n ∈ Z

x = n π + - 1 n 2 π 3 , where n ∈ Z

x = n π + - 1 n 3 π 3 , where n ∈ Z

MEDIUM

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Read the following statements.
(i) No non-living object exhibits metabolism.
(ii) Isolated metabolic reactions in vitro are living things.
(iii) Cellular organisation of the body is the defining feature of life forms.
(iv) Human beings including other mammals possess the property of self-consciousness.
How many of the statements are correct?

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Important Questions on Trigonometric Functions

MEDIUM

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

MEDIUM

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

\sec 4 θ = cosec (θ + 20^{o})

, then

θ

is equal to:

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

MEDIUM

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

The number of values of $α$ in $[0, 2 π]$ for which $2 \sin^{3} α - 7 \sin^{2} α + 7 sinα = 2$ , 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

EASY

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

The solution of

\sin x = - \frac{\sqrt{3}}{2}

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:

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 general solution of

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

for an integer

n

MEDIUM

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

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

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

EASY

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

The value of

\sin (45 ° + θ) - \cos (45 ° - θ)

is equal to

MEDIUM

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 .

HARD

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

The number of principal solutions of

\tan 2 θ = 1

is:

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

Important Questions on Trigonometric Functions

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