MyQuestionIcon

1

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

Product of Trigonometric Ratios in Terms of Their Sum

Prove that si...

Question

Prove that $s i n x + s i n 3 x + s i n 5 x + s i n 7 x = 4 c o s x c o s 2 x s i n 4 x .$

Open in App

Solution

We have LHS = $s i n x + s i n 3 x + s i n 5 x + s i n 7 x$

$= (s i n 7 x + s i n x) + (s i n 5 x + s i n 3 x)$

$= 2 s i n (\frac{7 x + x}{2}) c o s (\frac{7 x - x}{2}) + 2 s i n (\frac{5 x + 3 x}{2}) c o s (\frac{5 x - 3 x}{2})$

$[∵ s i n C + s i n D = 2 s i n (\frac{C + D}{2}) c o s (\frac{C + D}{2})]$

$= 2 s i n 4 X c o s 3 X + 2 s i n 4 X c o s x = 2 s i n 4 x (c o s 3 x + c o s x)$

$= 2 s i n 4 x \times 2 c o s (\frac{3 x + x}{2}) c o s (\frac{3 x - x}{2})$

$[∵ c o s C + c o s D = 2 c o s (\frac{C + D}{2}) o c s () \frac{C - D}{2}]$

$= 4 s i n 4 x c o s 2 x s i n 4 x = R H S H e n c e p r o v e d$

Suggest Corrections

thumbs-up

0

Similar questions

sin x + sin 3 x + sin 5 x + sin 7 x = 4 cos x cos 2 x sin 4 x

sin x + sin 3 x + sin 5 x + sin 7 x = 4 cos x cos 2 x sin 4 x

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

\frac{s i n x - s i n 3 x + s i n 5 x - s i n 7 x}{c o s x - c o s 3 x - c o s 5 x + c o s 7 x} = c o t 2 x

\frac{(sin 7 x + sin 5 x) + (sin 9 x + sin 3 x)}{(cos 7 x + cos 5 x) + (cos 9 x + cos 3 x)} = tan 6 x

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Transformations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Product of Trigonometric Ratios in Terms of Their Sum

Standard XI Mathematics

Join BYJU'S Learning Program

CrossIcon