The value of \(si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta } \) is equal to

(a)

 \(ta{ n }^{ 2 }\theta \)

(b)

1

(c)

\(cot^{ 2 }\theta \)

(d)

0

tan \(\theta \) cosec²\(\theta \) - tan\(\theta \) is equal to 

(a)

sec\(\theta \)

(b)

\(cot^{ 2 }\theta \)

(c)

sin\( \theta \)

(d)

\(cot\theta \)

If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

(a)

2a

(b)

3a

(c)

0

(d)

2ab

If 5x = sec\(\theta \) and \(\frac { 5 }{ x } \) = tan\(\theta \), then x² - \(\frac { 1 }{ { x }^{ 2 } } \) is equal to 

(a)

25

(b)

\(\frac { 1 }{ 25 } \)

(c)

5

(d)

1

If sin \(\theta \) = cos \(\theta \), then 2 tan² \(\theta \) + sin² \(\theta \) -1 is equal to 

(a)

\(\frac { -3 }{ 2 } \)

(b)

\(\frac { 3 }{ 2 } \)

(c)

\(\frac { 2 }{ 3 } \)

(d)

\(\frac { -2 }{ 3 } \)