Question

2. If 15 sina + 10cos^a = 6 then find the value
8 coseca +27 sec a.​

Answer 1

Answer:

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Answer 2

10sin4α+15cos4α=6

10(Sin4α+cos4α)+5cos4α=6

10((sin2α+cos2α)−2sin2αcos2α)±6−5cos4α

10(1−2sin2αcos2α)=6−5cos4α

4−20sin2αcos2α=−5cos4α

4sec4α−20tan2α=−5

20tan2α−4sec4α−5=0

20tan2α−4(1+tan2α)2−5=0

20tan2α−4(1+tan4α+2tan2α)−5=0

tan4α−3tan2α+49​=0

(tan2α−23​)2=0

tan2α=23​

tanα=2

​3

​​

Now 27cosec6α+8sec6α

(3cosec2α)3+(2sec2α)3

(3×35​)3+(2×25​)3

125+125

=250