Write the value of sin A-sin 3 A-cos A-cos 3 A

We have, sinA+sin3A/cosA+cos3A=sin3A+sinA/cos3A+cosA =2sin ( 3A+A/2 )cos ( 3A A/2 )/2cos ( 3A+A/2 )cos ( 3A A/2 ) =sin2A cosA/cos2A cosA=sin2A/cos2A=tan2A ∴ s ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

Write the val...

Question

Write the value of $\frac{s i n A + s i n 3 A}{c o s A + c o s 3 A}$

Open in App

Solution

We have,
$\frac{s i n A + s i n 3 A}{c o s A + c o s 3 A} = \frac{s i n 3 A + s i n A}{c o s 3 A + c o s A} = \frac{2 s i n (\frac{3 A + A}{2}) c o s (\frac{3 A - A}{2})}{2 c o s (\frac{3 A + A}{2}) c o s (\frac{3 A - A}{2})} = \frac{s i n 2 A c o s A}{c o s 2 A c o s A} = \frac{s i n 2 A}{c o s 2 A} = t a n 2 A ∴ \frac{s i n A + s i n 3 A}{c o s A + c o s 3 A} = t a n 2 A$

Suggest Corrections

Similar questions

\frac{{cos}^{3} A + {sin}^{3} A}{cos A + sin A} + \frac{{cos}^{3} A - {sin}^{3} A}{cos A - sin A}

Q. Prove that

\frac{S i n^{3} A + c o s^{3} A}{s i n A + c o s A} + \frac{S i n^{3} A - c o s^{3} A}{s i n A - c o s A} = 2

[4 MARKS]

Q. If

sin A + cos A = m

and

{sin}^{3} A + {cos}^{3} A = n

, then

Prove:

\frac{{c o s}^{3} A + {s i n}^{3} A}{c o s A + s i n A} + \frac{{c o s}^{3} A - {s i n}^{3} A}{c o s A - s i n A} = 2

Q. On simplifying

\frac{{sin}^{3} A + sin 3 A}{sin A} + \frac{{cos}^{3} A - cos 3 A}{cos A}

we get

Join BYJU'S Learning Program

Write the value of sinA+sin3AcosA+cos3A

We have, sinA+sin3AcosA+cos3A=sin3A+sinAcos3A+cosA=2sin(3A+A2)cos(3A−A2)2cos(3A+A2)cos(3A−A2)=sin2A cosAcos2A cosA=sin2Acos2A=tan2A∴ sinA+sin3AcosA+cos3A=tan2A

Write the value of $\frac{s i n A + s i n 3 A}{c o s A + c o s 3 A}$