Request a call back

Prove - sin5x-2sin3x+sinx /cos5x-cosx = tanx
Asked by prashant.jain | 24 May, 2010, 12:43: PM Expert Answer

We have explained the steps, please also refer to the solution in book, and apply the steps we listed below.

(sin5x-2sin3x+sinx) /(cos5x-cosx) =

In the numerator we can write for sin5x + sinx = 2 sin3x cos2x, using the result,

sinA + sinB = 2sin((A+B)/2)cos((A-B)/2), and here A = 5x and B = x.

Similarly for the denominator we can write,  cos5x - cosx = -2 sin3x sin2x,

cosA - cos B = -2sin((A+B)/2)sin((A-B)/2), and here A = 5x and B = x.

After this step, the next step is to take out sin3x common in numerator and denominator which cancels out leaving,

(1-cos2x)/sin2x,

Now make the final substitution using the trignometric results,

sin2A = 2sinAcosA and cos2A = cos2A - sin2A = 1 - 2sin2A.

After this substitution rest step is just algebraic manipulations to get the final result.

Regards,

Team,

TopperLearning.

Answered by | 24 May, 2010, 06:34: PM
CBSE 11-science - Maths
Asked by benganigaurav24 | 10 Jul, 2021, 10:05: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by sahabya | 29 May, 2010, 02:55: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by abhishek11 | 25 May, 2010, 07:11: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by prashant.jain | 24 May, 2010, 12:43: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by sidhusid | 18 May, 2010, 07:14: AM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by MANOJKUMAR | 16 May, 2010, 08:57: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by MANOJKUMAR | 15 May, 2010, 01:33: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by dandirao | 15 May, 2010, 12:19: PM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by prerana1994 | 11 May, 2010, 08:55: AM ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by varunsinghal2011 | 09 May, 2010, 03:45: PM ANSWERED BY EXPERT