Cos X + Cos 3X + Cos 5X Cos 7X Sin X + Sin 3X Sin 5X Sin 7X Cot 4X

     

\(\frac{sin\,x-sin\,3x+sin\,5x-sin\,7x}{cos\,x-cos\,3x-cos\,5x+cos\,7x}=cot\,2x\)

sin x- sin 3x+sin 5x-sin 7x/ co x-cos 3x-cos 5x+cos 7x = cot 2x


answeredFeb 10by ShubhamYadav(44.6k points)selectedFeb 11by Architakumari

L.H.S =\(\frac{sin\,x-sin\,3x+sin\,5x-sin\,7x}{cos\,x-cos\,3x-cos\,5x+cos\,7x}\)

=\(\frac{(5sin\,x + sin\,x)-(sin\,7x+sin\,3x)}{(cos\,x-cos5x)-(cos\,3x-cos\,7x)}\)

=\(\frac{2sin(\frac{5x+x}{2}).cos(\frac{5x-x}{2})-2sin(\frac{7x+3x}{2}).cos(\frac{7x-3x}{2})}{2sin(\frac{x+5x)}{2}).sin(\frac{5x-x}{2})-2sin(\frac{3x+7x}{2}).sin(\frac{7x-3x}{2})}\)

=\(\frac{2\,sin\,3x\,.cos\,2x-2\,sin\,5x.cos\,2x}{2\,sin\,3x.sin\,2x-2sin\,5x.sin\,2x}\)

=\(\frac{2\,cos\,2x(sin\,3x-sin\,5x)}{2\,sin\,2x(sin\,3x-sin\,\,5x)}\)

=\(\frac{cos\,2x}{sin\,2x}=cot\, 2x = R.H.S.\)


Please log in or register to add a comment.

Bạn đang xem: Cos x + cos 3x + cos 5x cos 7x sin x + sin 3x sin 5x sin 7x cot 4x


← Prev QuestionNext Question →

Find MCQs & Mock Test


Related questions


0 votes
1 answer
Express (cos 5x - cos 7x) as a product of sines or cosines.
askedMar 4in Trigonometryby Harshwardhan(24.1k points)
0 votes
1 answer
Evaluate , \(\rm \frac{\cos 7x\ +\ \cos 6x\ +\ \cos5x }{\sin 7x\ +\ \sin 6x\ +\ \sin 5x}\) .

Xem thêm: Nắng Đã Có Mũ Mưa Đã Có Ô - Nắng Đã Có Mũ, Mưa Đã Có Ô


askedMar 1in Trigonometryby VinayPoonia(53.1k points)
+1 vote
1 answer
Prove that (sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos 3x + cos 5x + cos 7x) = tan 4x
askedSep 17, 2020in Trigonometryby RamanKumar(50.2k points)
+6 votes
1 answer
Prove that <(sin 7x + sin 5x ) + (sin 9x + sin 3x )> / <(cos 7x + cos 5x ) + (cos 9x + cos 3x )> = tan 6x
*
askedDec 25, 2016in Mathematicsby sforrest072(128k points)
+6 votes
1 answer
Prove that sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x
*
askedDec 25, 2016in Mathematicsby sforrest072(128k points)

Welcome to xechieuve.com.vn eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Xem thêm: Cối Xay Gió Để Làm Gì - Những Điều Ít Người Biết Về Cối Xay Gió Hà Lan


Categories

Mathematics(236k)
User Contribution to xechieuve.com.vn eConnect
Managed by xechieuve.com.vn Digitizing India
...