10sin^4 theta + 15cos^4 theta = 6 , then fins the value of 27cosec^2 theta + 8sec^2theta
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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
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