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Trigonometric Functions

Multiple Choice Questions

131.

The value of $\cos (\frac{π}{5}) \cos (\frac{2 π}{5}) \cos (\frac{4 π}{5}) \cos (\frac{8 π}{5})$ will be

$\frac{1}{16}$
$- \frac{1}{16}$
0
$\frac{1}{2}$

132.

The function f(x) = sin(x) + cos(x) will be

an even function
an odd function
a constant function
None of these

133.

If $\sin (θ) + \csc (θ) = 2, then \sin^{2} (θ) + \csc^{2} (θ)$ is equal to

1
4
2
None of these

134.

The maximum value of $5 \cos (θ) + 3 \cos (θ + \frac{π}{3}) + 3$ is

10
- 10
14
None of these

135.

If $α and β$ are the solutions of $atan (θ) + bsec (θ) = c$ , then $\tan (α + β)$ is equal

$\frac{2 ac}{a^{2} - c^{2}}$
$\frac{2 ac}{c^{2} - a^{2}}$
$\frac{2 ac}{a^{2} + c^{2}}$
None of these

136.

If $\sin^{- 1} (\frac{x}{5}) + \csc^{- 1} (\frac{5}{4}) = \frac{π}{2}$ , then x is equal to

137.
If $\frac{\sin (A)}{\sin (C)} = \frac{\sin (A - B)}{\sin (B - C)}$ , then a², b², c² are in

AP

GP

HP

None of these

$\frac{\sin (A)}{\sin (C)} = \frac{\sin (A - B)}{\sin (B - C)} \frac{\sin (A)}{\sin (C)} = \frac{\sin (A) . \cos (B) - \cos (A) . \sin (B)}{\sin (B) . \cos (C) - \cos (B) . \sin (C)} \frac{aK}{cK} = \frac{aKcos (B) - bKcos (A)}{bKcos (C) - cKcos (B)} \{∵ \frac{\sin (A)}{a} = \frac{\sin (B)}{b} = \frac{\sin (C)}{c} = K\} \frac{a}{c} = \frac{acos (B) - bcos (A)}{bcos (C) - ccos (B)} \{∵ \cos (A) = \frac{b^{2} + c^{2} - a^{2}}{2 bc} \cos (B) = \frac{a^{2} + c^{2} - b^{2}}{2 ac} \cos (C) = \frac{a^{2} + b^{2} - c^{2}}{2 ab}\} \frac{a}{c} = \frac{\frac{(a^{2} + c^{2} - b^{2})}{2 c} - \frac{(b^{2} + c^{2} - a^{2})}{2 c}}{\frac{(a^{2} + b^{2} - c^{2})}{2 a} - \frac{(a^{2} + c^{2} - b^{2})}{2 a}}$

$= \frac{a}{c} [\frac{a^{2} + c^{2} - b^{2} - c^{2} - b^{2} + a^{2}}{a^{2} + b^{2} - c^{2} - a^{2} - c^{2} + b^{2}}] 1 = \frac{2 a^{2} - 2 b^{2}}{2 b^{2} - 2 c^{2}} \Rightarrow 1 = \frac{a^{2} - b^{2}}{b^{2} - c^{2}} \Rightarrow b^{2} - c^{2} = a^{2} - b^{2} \Rightarrow 2 b^{2} = a^{2} + b^{2} Hence, a^{2}, b^{2}, c^{2} are in AP .$

138.

If A = $60 °$ , a = 5, b = 4 $\sqrt{3}$ in $∆ ABC$ , then B is equal to

30°
60°
90°
None of these

139.

If y = sin²(x)cos²(x), then y_n is equal to

$(\frac{4^{n}}{8}) . \cos (4 x + \frac{nπ}{2})$
$({(- 1)}^{n} \frac{4^{n}}{8}) . \cos (4 x + \frac{nπ}{2})$
$(- \frac{4^{n}}{8}) . \cos (4 x + \frac{nπ}{2})$
None of the above

140.

In a $∆$ ABC, if cot(A) cot(B) cot(C) > 0, then the triangle is

acute angled
right angled
obtuse angled
does not exist

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

137. If sinAsinC = sinA - BsinB - C, then a2, b2, c2 are in AP GP HP None of these

137.
If $\frac{\sin (A)}{\sin (C)} = \frac{\sin (A - B)}{\sin (B - C)}$ , then a², b², c² are in

AP

GP

HP

None of these