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Let $A B C$ be a triangle with $4 \sin A = \sec B$ and $3 \tan A = \tan B$ . Then the triangle $A B C$ is

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Important Questions on Trigonometry - II

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

The value of

\cot \frac{π}{24}

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

(\cos^{2} θ + \frac{1}{c o s e c^{2} θ}) + 17 = x

, then what is the value of

x^{2}

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

\tan A = 1

and

\tan B = \sqrt{3}

, then

\cos (A + B)

is equal to

HARD

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

A B C D

is a trapezium such that

A B

and

C D

are parallel and

B C ⊥ C D

. If

∠ A D B = θ

B C = p

and

C D = q

, then

A B

is equal to

HARD

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

The value of

\sum_{k = 1}^{13} \frac{1}{\sin (\frac{π}{4} + \frac{(k - 1) π}{6}) \sin (\frac{π}{4} + \frac{k π}{6})}

is equal to

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

\frac{\cos (θ_{1} + θ_{2})}{\cos (θ_{1} - θ_{2})} + \frac{\cos (θ_{3} - θ_{4})}{\cos (θ_{3} + θ_{4})} = 0

, then

\cot θ_{1} \cdot \cot θ_{2} \cdot \cot θ_{3} \cdot \cot θ_{4} =

HARD

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

\tan (A - B) = \frac{1}{\sqrt{3}}

and

\tan (A + B) = \sqrt{3}

then the values of

A

and

B

are respectively

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

The maximum value of

\sin (x + \frac{π}{6}) + \cos (x + \frac{π}{6})

in the interval

(0, \frac{π}{2})

is attained at

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

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 multiples of

\frac{π}{2}

is-

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Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

A > 0, B > 0

and

A + B = \frac{π}{6}

, then the minimum positive value of

(\tan A + \tan B)

is :

HARD

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

When

\frac{\sin 9 θ}{\cos 27 θ} + \frac{\sin 3 θ}{\cos 9 θ} + \frac{\sin θ}{\cos 3 θ} = k (\tan 27 θ - \tan θ)

is defined, then

k =

HARD

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

The integer part of the number

\sum_{k = 0}^{44} \frac{1}{cosk ° \cos (k + 1) °}

(\sin 1 ° = 0.0174524)

HARD

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

0 < A < B < \frac{π}{4}, \cos (A + B) = \frac{11}{61}

and

\sin (A - B) = \frac{24}{25},

then

\sin 2 A + \sin 2 B =

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

Let

\cos (α + β) = \frac{4}{5}

and let

\sin (α - β) = \frac{5}{13}

, where

0 \leq α, β \leq \frac{π}{4}

, then

\tan 2 α =

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

\frac{\sin (A + B)}{\sin (A - B)} = \frac{\cos (C + D)}{\cos (C - D)}

, then

\tan A \cot B =

EASY

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

\tan (x + y) = 33

and

x = \tan^{- 1} 3

then

y

MEDIUM

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

Let

A, B

and

C

are the angles of a plain triangle and

\tan (\frac{A}{2}) = \frac{1}{3}, \tan (\frac{B}{2}) = \frac{2}{3}

Then,

\tan (\frac{C}{2})

is equal to

EASY

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

c o s (α + β) = \frac{3}{5}, \sin (α - β) = \frac{5}{13}

and

0 < α, β < \frac{π}{4},

then

\tan (2 α)

is equal to:

EASY

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

\sin 15^{o} =

EASY

Mathematics>Trigonometry>Trigonometry - II>Trigonometric Ratios of Sum-Difference of Angles

In a

Δ A B C

\frac{a}{b} = 2 + \sqrt{3}

, and

∠ C = 60 ° .

Then the ordered pair

(∠ A, ∠ B)

is equal to:

Let ABC be a triangle with 4sinA=secB and 3tanA=tanB. Then the triangle ABC is

Important Questions on Trigonometry - II

Learn and Prepare for any exam you want !

Let $A B C$ be a triangle with $4 \sin A = \sec B$ and $3 \tan A = \tan B$ . Then the triangle $A B C$ is