Questions on Trigonometry 31 Aug 2012 (Afternoon)
Question for practice
The following questions are more helpful for class tenth students for all boards.
Questions 21. If tanP - tanQ = a and cotQ - cotP = b, prove that cot(P - Q) = (1/a) + (1/b)
Submit your answer here in the comments or wait for answer
The following questions are more helpful for class tenth students for all boards.
Questions 21. If tanP - tanQ = a and cotQ - cotP = b, prove that cot(P - Q) = (1/a) + (1/b)
Submit your answer here in the comments or wait for answer
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ReplyDeletetanP - tanQ = a
ReplyDeletecotQ - cotP = b
LHS: (1/a)+(1/b)
= 1/(tanP - tanQ)+1/(cotQ - cotP)
= 1/(sinP/cosP - sinQ/cosQ)+1/(cosQ/sinQ - cosP/sinP)
= 1/{(sinPcosQ - cosPsinQ )/ cosPcosQ}+1/{(sinPcosQ - cosPsinQ )/sinPsinQ}
= cosPcosQ/(sinPcosQ - cosPsinQ)+ sinPsinQ/(sinPcosQ - cosPsinQ )
= (cosPcosQ + sinPsinQ) /( sinPcosQ - cosPsinQ)
= cos(P - Q)/sin (P - Q)
= cot(P - Q)
RHS = cot( P - Q)
Therefore , LHS = RHS
Hence, Proved.