10sin^4 theta + 15cos^4 theta = 6 , then fins the value of 27cosec^2 theta + 8sec^2theta
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Answer:
Step-by-step explanation:
For easier comprehension,
Let s=sinθ , c=cosθ
① Given equation→
10s^4+15c^4–6=0
(10s²)²+15(c²)²-6=0 ...S=s²
10S²+15(1-S)²-6=0
25S²-30S+9=0
(5S-3)²=0
5S=3
S=s²=3/5
c²=1-s²=4/5
② Given expression
=27csc²θ+8sec²θ
=27/s²+8/c²
=27*(5/3)+8*(5/4)
=45+10
=55
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