AIEEE 2010 | Trigonometric Ratio and Identites Question 47 | Mathematics

Let $$\cos \left( {\alpha + \beta } \right) = {4 \over 5}$$ and $$\sin \,\,\,\left( {\alpha - \beta } \right) = {5 \over {13}},$$ where $$0 \le \alpha ,\,\beta \le {\pi \over 4}.$$
Then $$tan\,2\alpha $$ =

$${56 \over 33}$$

$${19 \over 12}$$

$${20 \over 7}$$

$${25 \over 16}$$

AIEEE 2009

MCQ (Single Correct Answer)

-1

Let A and B denote the statements

A: $$\cos \alpha + \cos \beta + \cos \gamma = 0$$

B: $$\sin \alpha + \sin \beta + \sin \gamma = 0$$

If $$\cos \left( {\beta - \gamma } \right) + \cos \left( {\gamma - \alpha } \right) + \cos \left( {\alpha - \beta } \right) = - {3 \over 2},$$ then:

A is false and B is true

both A and B are true

both A and B are false

A is true and B is false

AIEEE 2006

MCQ (Single Correct Answer)

-1

If $$0 < x < \pi $$ and $$\cos x + \sin x = {1 \over 2},$$ then $$\tan x$$ is :

$${{\left( {1 - \sqrt 7 } \right)} \over 4}$$

$${{\left( {4 - \sqrt 7 } \right)} \over 3}$$

$$ - {{\left( {4 + \sqrt 7 } \right)} \over 3}$$

$${{\left( {1 + \sqrt 7 } \right)} \over 4}$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

Let $$\alpha ,\,\beta $$ be such that $$\pi < \alpha - \beta < 3\pi $$.
If $$sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}$$ and $$\cos \alpha + \cos \beta = - {{27} \over {65}}$$ then the value of $$\cos {{\alpha - \beta } \over 2}$$ :

$${{ - 6} \over {65}}\,\,$$

$${3 \over {\sqrt {130} }}$$

$${6 \over {65}}$$

$$ - {3 \over {\sqrt {130} }}$$

PREVIOUS NEXT

Questions Asked from Trigonometric Ratio and Identites (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions