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Trigonometry

Multiple Choice Questions

If $tan left parenthesis 5 straight x minus 10 degree right parenthesis space equals space cot space left parenthesis 5 straight y plus 20 degree right parenthesis$ , the value of (x + y) is

15°
16°
24°
24°

137 Views

The value of tan 11° tan 17° tan 79° tan 73° is

$1 half$
0
1
1

159 Views

(cos A + sin A)² + (cos A - sin A)² equals to

What is the value of $tan space open parentheses negative fraction numerator 5 straight pi over denominator 6 end fraction close parentheses$ ?

$negative fraction numerator 1 over denominator square root of 3 end fraction$
$fraction numerator 1 over denominator square root of 3 end fraction$
$square root of 3$
$negative square root of 3$

If cos C - cos D = x, then the value of x is

$2 space sin space open square brackets fraction numerator left parenthesis straight C plus straight D right parenthesis over denominator 2 end fraction space space COS fraction numerator left parenthesis straight C minus straight D right parenthesis over denominator 2 end fraction close square brackets$
$2 space cos space open square brackets fraction numerator left parenthesis straight C plus straight D right parenthesis over denominator 2 end fraction close square brackets space sin space open square brackets fraction numerator left parenthesis straight D minus straight C right parenthesis over denominator 2 end fraction close square brackets$
$2 sin open square brackets fraction numerator open parentheses straight C plus straight D close parentheses over denominator 2 end fraction close square brackets space sin space open square brackets fraction numerator open parentheses straight D minus straight C close parentheses over denominator 2 end fraction close square brackets$
$2 space cos space open square brackets fraction numerator open parentheses straight C plus straight D close parentheses over denominator 2 end fraction close square brackets space cos space open square brackets fraction numerator open parentheses straight C minus straight D close parentheses over denominator 2 end fraction close square brackets$

Find the value of $open parentheses fraction numerator sin space 27 degree over denominator cos space 63 degree end fraction close parentheses squared space plus space open parentheses fraction numerator cos space 63 degree over denominator sin space 27 degree end fraction close parentheses squared$

304 Views

The value of the following is:
$cos space 24 degree space plus space cos space 55 degree space plus space cos space 125 degree space plus space cos space 204 degree space plus space cos space 300 degree$

2
$1 half$
1
1

259 Views

If tan A + cot A = 2, then the value of $tan to the power of 10 straight A space plus cot to the power of 10 straight A$ is

1
4
$2 to the power of 10$
$2 to the power of 10$

239 Views

9.
If $fraction numerator secθ plus tanθ over denominator secθ minus tanθ end fraction space equals space 2 51 over 79 comma$ then the value of $sinθ$ is

$39 over 72$
$35 over 72$
$65 over 144$
$65 over 144$

65 over 144

fraction numerator secθ plus tanθ over denominator secθ minus tanθ end fraction equals 5 over 3

Apply C & D

rightwards double arrow space space fraction numerator left parenthesis secθ plus tanθ right parenthesis space plus space left parenthesis secθ minus tanθ right parenthesis over denominator left parenthesis secθ plus tanθ right parenthesis minus left parenthesis secθ minus tanθ right parenthesis end fraction space equals space 209 over 79 rightwards double arrow space space space space fraction numerator 2 secθ over denominator 2 tanθ end fraction space equals space fraction numerator 209 plus 79 over denominator 209 minus 79 end fraction space equals space 288 over 130 space equals space 144 over 65 rightwards double arrow space fraction numerator begin display style 1 over cosθ end style over denominator begin display style sinθ over cosθ end style end fraction space equals space 4 space space space rightwards double arrow space space space space fraction numerator 1 over denominator sin space straight theta end fraction space equals space 144 over 65

So,

sin space straight theta space equals space 65 over 144

231 Views

10.

If $1 plus cos squared straight theta space equals space 3 space sin space straight theta space cosθ comma$ then find the integral value of $cot space straight theta$ is $open parentheses 0 less than straight theta less than straight pi over 2 close parentheses$