Express the product as a sum containing only sines or cosines.cos (4 ) cos (8 )
Question
Express the product as a sum containing only sines or cosines.
Solution
The product of cos(4) and cos(8) can be expressed as a sum containing only sines or cosines using the product-to-sum identities in trigonometry. The relevant identity here is:
cos(A)cos(B) = 1/2[cos(A - B) + cos(A + B)]
Applying this identity to the given expression, we get:
cos(4)cos(8) = 1/2[cos(4 - 8) + cos(4 + 8)] = 1/2[cos(-4) + cos(12)] = 1/2[cos(4) + cos(12)]
So, cos(4)cos(8) can be expressed as 1/2[cos(4) + cos(12)].
Similar Questions
(ii) Convert the products of sine A and cos C into the sum form of trigonometric functions of the triangle above.
Use the sum-to-product identities to rewrite the following expression in terms containing only first powers of tangent. sin8x−sin2xcos8x+cos2x
Use the sum and difference identities to determine the exact value of the following expression.sin(2π3−π4)
Making this substitution using16 sin2(x) cos3(x) dxgives us 16 sin2(x) (1 − sin2(x)) cos(x) dx = 16 sin2(x) cos(x) dx − cos(x) dx.
Which of the following trigonometric function is involved in cross product?Group of answer choicessinetangentcotangentcosine
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.