Grade 12th passTrigonometry
prove sina+sin3a+sin5a+sin7a/cosacos3a+cos5a+tan7a=tan4a
prove sina+sin3a+sin5a+sin7a/cosacos3a+cos5a+tan7a=tan4a
1 Answer
Vikas TU
Dear student
SinA+sin3A+sin5A+sin7A/cosA+cos3A+cos5A+cos7A
=(sinA+sin7A)+(sin3A+sin5A)/(cosA+cos7A)+(cos3A+cos5A)
=(2sin4Acos3A+2sin4AcosA)/(2cos4Acos3A+2cos4AcosA)
=2sin4A(cos3A+cosA)/2cos4A(cos3A+cosA)
=sin4A/cos4A
=tan4A (Proved)
=(sinA+sin7A)+(sin3A+sin5A)/(cosA+cos7A)+(cos3A+cos5A)
=(2sin4Acos3A+2sin4AcosA)/(2cos4Acos3A+2cos4AcosA)
=2sin4A(cos3A+cosA)/2cos4A(cos3A+cosA)
=sin4A/cos4A
=tan4A (Proved)
Hope this helps
Good Luck
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