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| 1. |
sin11asin7a+sinasin3a/cos11asin3a+cos7asina=tan8a prove this |
| Answer» 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 | |