Trigonometric Functions Test 35

Result

Trigonometric Functions Test 35

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Weekly Quiz Competition

Question 1
1 / -0

Choose the correct answer.
$$(1+{ \tan }^{ 2 }\theta ){ \sin }^{ 2 }\theta =$$

A
$${ \tan }^{ 2 }\theta $$

B
$${ \cot }^{ 2 }\theta $$

C
$${ \sin }^{ 2 }\theta $$

D
$${ \cos }^{ 2 }\theta $$

Solution
Question 2
1 / -0

The value of $$\sum\limits_{r = 0}^9 {{{\sin }^2}\dfrac{{\pi r}}{{18}}} \;is\;equal\;to\;$$

A
$$\dfrac{9}{2}$$

B
$$\dfrac{7}{2}$$

C
5

D
None of these

Solution
Question 3
1 / -0

If $$\sqrt { 2 } sin\theta -\sqrt { 2 } cos\theta +1=0$$ and $$\theta $$ is an acute angle, then the value of $$cosec\theta $$ is

A
$$2(\sqrt { 2 } +1)$$

B
$$\sqrt { 2 } (\sqrt { 3 } +1)$$

C
$$\cfrac { \sqrt { 2 } +1 }{ 2 } $$

D
$$\cfrac { -(\sqrt { 3 } +1) }{ 2 } $$

Solution
Question 4
1 / -0

If $$\frac{1+cos\Theta }{1-cos\Theta }=\frac{p^{2}}{q^{2}}$$ then $$tan \Theta $$ =

A
$$\frac{2pq}{p^{2}-q^{2}}$$

B
$$\pm \frac{2pq}{p^{2}+q^{2}}$$

C
$$\pm \frac{2pq}{p^{2}-q^{2}}$$

D
$$\frac{p^{2}+q^{2}}{p^{2}-q^{1}}$$

Solution
Question 5
1 / -0

The principal solutions of $$secx= \frac{2}{\sqrt{3}}$$ are _________

A
$$\frac{\pi }{3},\frac{||\pi }{6}$$

B
$$\frac{\pi }{6},\frac{11\pi }{6}$$

C
$$\frac{\pi }{4},\frac{||\pi }{4}$$

D
$$\frac{\pi }{6},\frac{||\pi }{4}$$

Solution
Question 6
1 / -0

The value of $$\frac{cosA}{P1}+\frac{cosB}{P2}+\frac{cosC}{p3}$$

A
$$\frac{1}{r}$$

B
$$\frac{1}{R}$$

C
$$\frac{a^{2}+b^{2}+c^{2}}{2R}$$

D
$$\frac{1}{\Delta }$$
Question 7
1 / -0

If the equitation $$1+sin^{2}px=cos x$$ has exactly one solution then p is ______

A
any real number

B
any irrational number

C
any rational number

D
None of these

Solution
Question 8
1 / -0

32 $$sin^{6}15^{0}-48sin^{4}15^{0}+18sin^{2}15^{0}=$$

A
1

B
2

C
3

D
-1

Solution
Question 9
1 / -0

If $$sec A=a+(\frac{1}{4a})$$ , then sec A + tan A is equal to

A
$$2a \;or\; \frac{1}{2a}$$

B
$$a or \frac{1}{a}$$

C
$$2a or\frac{1}{a}$$

D
$$a or \frac{1}{2a}$$

Solution
Question 10
1 / -0

If $$tan\Theta +cot\Theta =3$$ , find the value of $$tan^{2\Theta }+sin^{2\Theta }$$

A
5

B
3

C
7

D
11

Solution