Question

If sec theta + tan theta = 2, then find the value of sec5 theta + tan5 theta .

Answer 1

Answer:

secθ+tanθ=2+

5

secθ−tanθ=

2+

5

1

=

5

+2

1

×

5

−2

5

−2

=

5

−2=

5

−2

secθ−tanθ=

5

−2⇒2secθ=2

5

secθ=

5

⇒cosθ=

5

1

sin

2

θ=1−cos

2

θ=1−(

5

1

)

2

=1−

5

1

=

5

4

⇒sinθ=

5

2

.