Question

if 10sin thita =6 find value of cos^2 theta + sin^2 theta /tan^2theta + sin^2theta​

Answer 1

Answer:

10sin4α+15cos4α=6

10(Sin

4

α+cos

4

α)+5cos

4

α=6

10((sin

2

α+cos

2

α)−2sin

2

αcos

2

α)±6−5cos

4

α

10(1−2sin

2

αcos

2

α)=6−5cos

4

α

4−20sin

2

αcos

2

α=−5cos

4

α

4sec

4

α−20tan

2

α=−5

20tan

2

α−4sec

4

α−5=0

20tan

2

α−4(1+tan

2

α)

2

−5=0

20tan

2

α−4(1+tan

4

α+2tan

2

α)−5=0

tan

4

α−3tan

2

α+

4

9

=0

(tan

2

α−

2

3

)

2

=0

tan

2

α=

2

3

tanα=

2

3

Now 27cosec

6

α+8sec

6

α

(3cosec

2

α)

3

+(2sec

2

α)

3

(3×

3

5

)

3

+(2×

2

5

)

3

125+125

=250