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Trigonometry

Multiple Choice Questions

41.

a, b, c are the lengths of three sides of a triangle ABC. If a, b, c are related by the relation a² + b² + c² = ab + bc + ca, then the value of sin²A+ sin²B + sin²C is

$3 over 4$
$fraction numerator 3 square root of 3 over denominator 2 end fraction$
$3 over 2$
$3 over 2$

247 Views

42.

The value of $straight theta space left parenthesis 0 space less or equal than space straight theta space less or equal than space 90 degree right parenthesis$ satisfying $2 space sin squared straight theta space equals space 3 space cosθ$ is

$60 degree$
$30 degree$
$90 degree$
$90 degree$

166 Views

43.

If $tan space straight x space equals space sin space 45 degree. space cos space 45 degree space plus space sin space 30 degree$ then the value of x is

$30 degree$
$45 degree$
$60 degree$
$60 degree$

128 Views

44.
For any real values of θ, $fraction numerator square root of secθ space minus 1 end root over denominator square root of secθ space plus 1 end root end fraction space equals space ?$

$cot space straight theta space minus space cosec space straight theta$
$secθ space minus space tanθ$
$cosecθ space minus space cotθ$
$cosecθ space minus space cotθ$

cosecθ space minus space cotθ

Shortcut method:
Put any value of θ in the question which matches with option for ex:
Put θ = 60°

rightwards double arrow space space square root of fraction numerator sec space 60 degree space minus space 1 over denominator sec space 60 degree space plus 1 end fraction end root space equals space square root of fraction numerator 2 minus 1 over denominator 2 plus 1 end fraction end root space equals space square root of 1 third end root space equals space fraction numerator 1 over denominator square root of 3 end fraction

In the option (3) let's put value of θ = 60°

space equals space space cosec space 60 degree space minus space cot space 60 degree equals space fraction numerator 2 over denominator square root of 3 end fraction space minus space fraction numerator 1 over denominator square root of 3 end fraction space equals space fraction numerator 1 over denominator square root of 3 end fraction

250 Views

45.

If sin 3A = cos (A - 26°), where 3A is an acute angle then the value of A is

29°
26°
23°
23°

178 Views

46.

Find the value of $sec squared straight theta space minus space fraction numerator sin squared straight theta space minus space 2 sin to the power of 4 straight theta over denominator 2 cos to the power of 4 straight theta space minus space cos squared straight theta end fraction$

1
2
-1
-1

153 Views

47.

If x = a(sinθ + cosθ), y = b(sinθ - cosθ) then the value of $straight x squared over straight a squared space plus space straight y squared over straight b squared$ is

202 Views

48.

If sin 5θ = cos 20° (0° < θ < 90°) then the value of θ is

4°
22°
10°
10°

140 Views

49.

ABCD is a rectangle of which AC is a diagonal. The value of is

183 Views

50.

In a Δ ABC, $angle straight B space equals space straight pi over 3 comma space space angle straight C space equals space straight pi over 4$ and D divides BC internally in the ratio 1 : 3 then $fraction numerator sin space angle BAD over denominator sin space angle CAD end fraction$ is equal to