21)

The value of \({sin\theta+cos\theta-1\over sin\theta-cos\theta+1}\times\)\({ tan^2\theta(cosec^2\theta-1)\over sec\theta-tan\theta}\) is :

SSC CGL 2019

A)

0

B)

-1

C)

1

D)

\(\frac{1}{2}\)

22)

If \({sin\theta\over1+cos\theta}+\)\({1+cos\theta\over sin\theta}\)\(={4\over \sqrt3}\), \(0^0<\theta<90^0\), then the value of \((tan\theta+sec\theta)^{-1}\) is :

SSC CGL 2019

A)

\(2-\sqrt3\)

B)

\(3-\sqrt2\)

C)

\(2+\sqrt3\)

D)

\(3+\sqrt2\)

23)

If \({1+sin\theta\over1-sin\theta}={p^2\over q^2}\), then \(sec\theta\) is equal to :

SSC CGL 2019

A)

\(2p^2q^2\over p^2+q^2\)

B)

\({1\over2}({q\over p}+{p\over q})\)

C)

\({1\over p^2}+{1\over q^2}\)

D)

\(p^2q^2\over p^2+q^2\)

24)

The value of \(sec\theta(1-sin\theta)(sin\theta+cos\theta)(sec\theta+tan\theta)\over sin\theta(1+tan\theta)+cos\theta(1+cot\theta)\) is equal to :

SSC CGL 2019

A)

\(2cos\theta\)

B)

\(cosec\theta sec\theta\)

C)

\(2sin\theta\)

D)

\(sin\theta cos\theta\)

25)

The value of \((tan^2\theta+cot^2\theta-sec^2\theta cosec^2\theta)\) is equal to :

SSC CGL 2019

A)

-2

B)

1

C)

0

D)

-1

26)

\((sec\theta-tan\theta)^2(1+sin\theta)^2\div sin^2\theta=?\)

SSC CGL 2019

A)

\(cos\theta\)

B)

\(cot^2\theta\)

C)

\(sec\theta\)

D)

\(cos^2\theta\)

27)

If \(3(cot^2\theta-cos^2\theta)=cos^2\theta\), \(0^0<\theta<90^0\), then the value of \((tan^2\theta+cosec^2\theta+sin^2\theta)\) is :

SSC CGL 2019

A)

\(13\over3\)

B)

\(61\over12\)

C)

\(25\over12\)

D)

\(15\over4\)

28)

If \({sin^2\theta-3sin\theta+2\over cos^2}=1\), where \(0^0<\theta<90^0\), then what is the value of \((cos2\theta+sin3\theta\)\(+cosec2\theta)\) ?

SSC CGL 2019

A)

\(2+\sqrt3\over3\)

B)

\(3+4\sqrt3\over6\)

C)

\(9+4\sqrt3\over6\)

D)

\(3+2\sqrt3\over3\)

29)

The value of \(sin(78^0+\theta)-cos(12^0-\theta)+(tan^270^0-cosec^220^0)\over sin25^0cos65^0+cos25^0sin65^0\) is :

SSC CGL 2019

A)

2

B)

-1

C)

-2

D)

0

30)

The value of \(\sqrt{cosec\theta-cot\theta\over cosec\theta+cot\theta}\)\(\div {sin\theta\over1+cos\theta}\) is equal to :

SSC CGL 2019

A)

\(cosec\theta\)

B)

\(1\over2\)

C)

\(sec\theta\)

D)

1