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21.
If $sec space straight theta space equals space cosec space straight ϕ$ with $0 degree less than space straight theta comma space space straight ϕ space less than space 90 degree$ , then the value of $sin left parenthesis straight theta plus straight ϕ right parenthesis$ is

1

0

2

2

secθ space equals space cosecϕ

1 over cosθ equals space fraction numerator 1 over denominator sin begin display style space end style begin display style straight ϕ end style end fraction

sin space straight ϕ space equals space cos space straight theta sin space straight ϕ space equals space sin left parenthesis 90 degree minus straight theta right parenthesis space space space space straight ϕ space equals space 90 degree minus straight theta straight theta plus straight ϕ space equals space 90 degree

therefore space sin space left parenthesis straight theta space plus space straight ϕ right parenthesis space equals space sin space 90 degree space equals space 1

181 Views

22.

If in a triangle ABC, sinA = cosB then the value of cos C is

$fraction numerator square root of 3 over denominator 2 end fraction$
0
1
1

155 Views

23.

If $sin space straight theta space cross times space cos space straight theta space equals space 1 half comma space$ the value of $sin space straight theta space minus space cos space straight theta$ is (where $0 degree less than straight theta less than 90 degree$ ):

0
$square root of 2$
2
2

137 Views

24.

The value of $fraction numerator sinθ over denominator 1 plus cosθ end fraction plus fraction numerator sin begin display style straight theta end style over denominator 1 minus cosθ end fraction$ is

$2 sinθ$
$2 cosθ$
$2 secθ$
$2 secθ$

172 Views

25.

If $tan space straight theta space equals space 8 over 15 comma$ the value of $fraction numerator square root of 1 minus sin space straight theta end root over denominator square root of 1 plus sin space straight theta end root end fraction$ is

$1 fifth$
$2 over 5$
$3 over 5$
$3 over 5$

207 Views

26.

If $fraction numerator cosθ space over denominator 1 minus sinθ end fraction plus fraction numerator cos begin display style space end style begin display style straight theta end style over denominator 1 plus sin space straight theta end fraction space equals space 4$ then the value of $straight theta$ $left parenthesis 0 less than straight theta less than 90 degree right parenthesis$ is

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

199 Views

27.

If $straight x space equals space straight a space cosθ space plus space straight b space sinθ$ and $straight y equals straight b space cosθ space minus space straight a space sinθ$ , then $straight x squared plus straight y squared$ is equal to

ab
$straight a squared plus straight b squared$
$straight a squared minus straight b squared$
$straight a squared minus straight b squared$

228 Views

28.

If x tan 60° + cos 45° = sec 45° then the value of (x² + 1) is

$6 over 7$
$7 over 6$
$5 over 6$
$5 over 6$

502 Views

29.

x, y be two acute angles, x + y < 90° and sin (2x - 20°) = cos (2y + 20°), the value of tan (x + y) is

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

721 Views

30.

If a²sec²x - b²tan²x = c² then the value of (sec²x + tan²x) is equal to (assume b² ≠ a²)

$fraction numerator straight b squared minus straight a squared plus 2 straight c squared over denominator straight b squared plus straight a squared end fraction$
$fraction numerator straight b squared plus straight a squared minus 2 straight c squared over denominator straight b squared minus straight a squared end fraction$
$fraction numerator straight b squared minus straight a squared minus 2 straight c squared over denominator straight b squared plus straight a squared end fraction$
$fraction numerator straight b squared minus straight a squared minus 2 straight c squared over denominator straight b squared plus straight a squared end fraction$