(SinA + Sin3A + Sin5A + Sin7A)/(CosA + Cos3A + Cos5A + Tan7A) = tan 4A
Anil Karira , 4 Years ago
Grade 12th pass
Trigonometry> (SinA + Sin3A + Sin5A + Sin7A)/(CosA + Co...
2 Answers
Saurabh Koranglekar
Last Activity: 4 Years ago
Dear student
Please write complete question is it to prove or finding value of A
Regards
Aditya Gupta
Last Activity: 4 Years ago
(sinA+sin3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A)
=(sinA+sin7A)+(sin3A+sin5A)/(cosA+cos7A)+(cos3A+cos5A)
=(2sin4Acos3A+2sin4AcosA)/(2cos4Acos3A+2cos4AcosA) (using sinx + siny= 2sin(x+y)/2cos(x – y)/2 and cosx + cosy= 2cos(x+y)/2cos(x – y)/2)
=2sin4A(cos3A+cosA)/2cos4A(cos3A+cosA)
=sin4A/cos4A
=tan4A
=(sinA+sin7A)+(sin3A+sin5A)/(cosA+cos7A)+(cos3A+cos5A)
=(2sin4Acos3A+2sin4AcosA)/(2cos4Acos3A+2cos4AcosA) (using sinx + siny= 2sin(x+y)/2cos(x – y)/2 and cosx + cosy= 2cos(x+y)/2cos(x – y)/2)
=2sin4A(cos3A+cosA)/2cos4A(cos3A+cosA)
=sin4A/cos4A
=tan4A
hence proved
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