prove that tan 255 degree × cot 405 degree + tan 765 degree × cos 675 degree =0
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Taking LHS,
tan 2250 * cot 4050 + tan 7650 * cot 6750
Now tan 225 = tan(180+45)= tan 45 = 1
cot 405 = cot(360+45)= cot 45 = 1
tan 765= tan(720+45 )= tan 45 =1
cot 675 = cot(720-45)= -cot 45 = -1
Putting all thee values we get,
1×1−1×1=0
RHS
tan 2250 * cot 4050 + tan 7650 * cot 6750
Now tan 225 = tan(180+45)= tan 45 = 1
cot 405 = cot(360+45)= cot 45 = 1
tan 765= tan(720+45 )= tan 45 =1
cot 675 = cot(720-45)= -cot 45 = -1
Putting all thee values we get,
1×1−1×1=0
RHS
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