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Hard Trigonometrical identities and trigonometrical functions MCQs for JEE

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Hard Trigonometrical identities and trigonometrical functions MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (32+ on Goodmarks).

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Part of Trigonometry in JEE Main Mathematics.

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Q1MathsUnit 14: Trigonometry

\mathbf{A}=\cos 20^{0} \cos 40^{0} \cos 60^{0} \cos 80^{0}

\mathbf{B}=\cos 6^{0} \cos 42^{0} \cos 66^{0} \cos 78^{0}

\mathbf{C}=\cos \mathbf{3} \mathbf{6}^{\mathbf{0}} \cos \mathbf{7} \mathbf{2}^{\mathbf{0}} \cos \mathbf{1 0} \mathbf{8}^{\mathbf{0}} \cos \mathbf{1} \mathbf{4} \mathbf{4}^{\mathbf{0}}

Q2MathsUnit 14: Trigonometry

The measures of the angles of a triangle are in the ratio

4: 5: 9 .

The triangle is:

Q3MathsUnit 14: Trigonometry

\ln \Delta A B C, B C=A B

and

\angle B=80^{\circ}

Then

\angle A

is equal to

Q4MathsUnit 14: Trigonometry

Two line segments

A B

and

A C

include an angle of

60^{0}

where

A B=5 \mathrm{cm}

and

A C

=7 \mathrm{cm} .

Locate points

\mathrm{P}

and

\mathrm{Q}

\mathrm{AB}

and

A C,

respectively such that

A P=\frac{3}{4}

A B

and

A Q=\frac{1}{4} A C .

Join

P

and

Q

and measure the length PQ.

Q5MathsUnit 14: Trigonometry

The terminal arm is in II quadrant, what are the measures of possible angles?

Q6MathsUnit 14: Trigonometry

\tan \theta=\frac{x \sin \phi}{1-x \cos \phi}, \tan \phi=

\frac{y \sin \theta}{1-y \cos \theta},

then

\frac{x}{y}=

Q7MathsUnit 14: Trigonometry

\sqrt{\frac{1-\sin A}{1+\sin A}}+\frac{\sin A}{\cos A}=\frac{1}{\cos A},

for all permissible values of

A,

then

A

belongs to This question has multiple correct options

Q8MathsUnit 14: Trigonometry

If two triangles are

_{--}-

they are similar.

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