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Asked by rbhatt16 12th October 2017, 5:03 PM
Answered by Expert
Answer:
begin mathsize 16px style According space to space the space question
straight d space equals space straight theta subscript 2 space minus space straight theta subscript 1 space equals straight theta subscript 3 space minus space straight theta subscript 2 space equals................... left parenthesis straight i right parenthesis
LHS space equals space sind space open parentheses sec straight theta subscript 1 space sec space straight theta subscript 2 space plus secθ subscript 2 space sec space straight theta subscript 3 space plus.......... plus secθ subscript straight n space sec space θn minus 1 close parentheses
equals fraction numerator sind over denominator cosθ subscript 1 space cos space straight theta subscript 2 end fraction plus fraction numerator sind over denominator cosθ subscript 1 space cos space straight theta subscript 2 end fraction space plus.... plus fraction numerator sind over denominator cosθ subscript straight n space cos space straight theta subscript straight n minus 1 end subscript end fraction
equals fraction numerator sin open parentheses space straight theta subscript 2 space minus space straight theta subscript 1 close parentheses over denominator cosθ subscript 1 space cos space straight theta subscript 2 end fraction plus fraction numerator sin open parentheses straight theta subscript 3 space minus space straight theta subscript 2 space close parentheses over denominator cosθ subscript 1 space cos space straight theta subscript 2 end fraction space plus.... plus fraction numerator sin open parentheses straight theta subscript straight n space minus space straight theta subscript straight n minus 1 end subscript space close parentheses over denominator cosθ subscript straight n space cos space straight theta subscript straight n minus 1 end subscript end fraction
After space using space formula space sin space left parenthesis straight A minus straight B right parenthesis equals sinAcosB minus cosAsinB
You space will space get space
equals tan space straight theta subscript 1 space minus space tan space space straight theta subscript straight n


For space teh space second space question space use space property space of space AP space and space simplify space it space further space
you space will space get space the space answer.
end style
Answered by Expert 19th December 2017, 5:39 PM
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