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If cos(alpha+beta)+sin(alpha-beta)=0 and...

If `cos(alpha+beta)+sin(alpha-beta)=0` and `tan beta ne1`, then find the value of `tan alpha`.

Text Solution

Verified by Experts

The correct Answer is:
`-1`
`cos alpha cos beta-sin alpha sin beta+sin alpha cos beta-cos alpha sin beta=0`
`rArr cos alpha(cos beta-sin beta)+sinalpha(cos beta-sibeta)=`
`rArr (cos beta-sin beta)(cos alpha+sin alpha)=0`
If `cos beta-sin beta=0`, then `tan beta=1`, which is not possible
`therefore sin alpha+cos alpha=0`
`therefore sin 3A=-59//72`.
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