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Two tangents are drawn from a point P to a circle at A and B. O is the centre of the circle. If \angle $ AOP = 60^{\circ} $ , then $ \angle APB $ is:

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Important Questions on Trigonometric Ratios and Identities

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

In the right triangle shown in the figure, what is the value of

\cos e c θ

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

5 \sin (θ) = 4

, then the value of

\frac{secθ + 4 cotθ}{4 tanθ - 5 cosθ}

is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Solve the following.

\sin 0 ° \sin 30 ° \sin 45 ° \sin 60 ° \sin 90 ° = ?

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

From a point exactly midway between the foot of two towers

P

and

Q

, the angle of elevation of their tops are

30^{°}

and

60^{°}

, respectively. The ratio of the height of

P

to that of

Q

is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

\frac{\sin θ}{1 - \cot θ} + \frac{\cos θ}{1 - \tan θ} =

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

\frac{cosec 31 °}{\sec 59 °}

is equal to_____.

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The value of

\frac{\sin 30 ° \sin 60 °}{\cos 60 ° \cos 30 °} - \tan 45 °

is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The value of

(\frac{\sin (A)}{1 - \cos (A)} + \frac{1 - \cos (A)}{\sin (A)}) \div (\frac{\cot^{2} (A)}{1 + \csc (A)} + 1)

is______.

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The value of

(\cos e c 30 ° - \tan 45 °) c o t 60 ° \tan 30 °

is:

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The value of

\cos 10 ° \cos 30 ° \cos 50 ° \cos 70 ° \cos 90 °

is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Find the value of following equation:

${(\sec \emptyset - \tan \emptyset)}^{2} {(1 + \sin \emptyset)}^{2} \div \sin^{2} \emptyset = ?$

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

What is the simplified value of

{(\frac{1}{cosec A + \cot A})}^{2}

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

3 (\cot^{2} (ϕ) - \cos^{2} (ϕ)) = \cos^{2} (ϕ)

0 ° < ϕ < 90 °

, then the value of

(\tan^{2} (ϕ) + \csc^{2} (ϕ) + \sin^{2} (ϕ))

is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

Solve the following.

(\frac{\sin 27 °}{\cos 63 °}) - {(\frac{\cos 27 °}{\sin 63 °})}^{2}

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

The value of

\frac{\sec (ϕ) (1 - \sin (ϕ)) (\sin (ϕ) + \cos (ϕ)) (\sec (ϕ) + \tan (ϕ))}{\sin (ϕ) (1 + \tan (ϕ)) + \cos (ϕ) (1 + \cot (ϕ))}

is equal to:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

\sin (18 °) - \cos (72 °)

is equal to:

MEDIUM

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

(\cos θ + \sin θ) : (\cos θ - \sin θ) = (\sqrt{3} + 1) : (\sqrt{3} - 1)

0^{\circ} < θ < 90^{\circ}

, then what is the value of

\sec θ ?

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

What is the value of

\frac{cosec (78^{o} + θ) - \sec (12^{o} - θ) - \tan (67^{o} + θ) + \cot (23^{o} - θ)}{\tan 13^{o} \tan 37^{o} \tan 45^{o} \tan 53^{o} \tan 77^{o}}

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

If $3 \sin θ = 2 \cos^{2} θ, 0^{0} < θ < 90^{0}$ . Then the value of $(\tan^{2} θ + s e c^{2} θ - \cos e c^{2} θ)$ is:

EASY

Mathematics>Trigonometry>Trigonometric Ratios and Identities>Basics of Trigonometry

\cos^{2} θ - \sin θ = \frac{1}{4}

, then what is the value of

\sin θ

Two tangents are drawn from a point P to a circle at A and B. O is the centre of the circle. If \angle \( AOP = 60^{\circ} \) , then \( \angle APB \) is:

Important Questions on Trigonometric Ratios and Identities

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