If tan⁡α2 and tan⁡β2 are the roots of the equation 8x2−26x+15=0, then cos⁡(α+β)=

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−627725

627725

-1

none of these

answer is A.

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Detailed Solution

We have,tan⁡α2+tan⁡β2=134 and tan⁡α2tan⁡β2=158tan⁡α2+β2=tan⁡α2+tan⁡β21−tan⁡α2tan⁡β2=267Now,cos⁡(α+β)=1−tan2⁡α+β21+tan2⁡α+β2=1−676191+67649=−627725

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