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sin11asin7a+sinasin3a/cos11asin3a+cos7asina=tan8a prove this

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sin11asin7a+sinasin3a/cos11asin3a+cos7asina=tan8a prove this

Posted by Tanvi Chauhan?? 4 years, 10 months ago

CBSE > Class 11 > Mathematics

1 answers

Sia ? 4 years, 10 months ago

sin11asina+sin7asin3a/cos11asina+cos7asin3a
=2sin11asina+2sin7asin3a/2cos11asina+2cos7asin3a
=[{cos(11a-a)-cos(11a+a)}+{cos(7a-3a)-cos(7a+3a)}]/
[{sin(11a+a)-sin(11a-a)}+{sin(7a+3a)-sin(7a-3a)}]
=(cos10a-cos12a+cos4a-cos10a)/(sin12a-sin10a+sin10a-sin4a)
=(cos4a-cos12a)/(sin12a-sin4a)
=[2sin(4a+12a)/2sin(12a-4a)/2]/[2cos(12a+4a)/2sin(12a-4a)/2]
=sin8asin4a/cos8asin4a
=sin8a/cos8a
=tan 8a

1Thank You

ANSWER

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CBSE > Class 11 > Mathematics