The trigonometric expression (1+cos(x))2(tan(x/2)) is equivalent to (1+cos(x))(sin(x)) option (d) is correct.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
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It is given that:
The trigonometric expression is:
= (1+cos(x))²(tan(x/2))
As we know,
1 + cos(x) = 2cos²(x/2)
Use the above trigonometric identity:
= (2cos²(x/2))²(tan(x/2))
= 2 cos⁴(x/2) sin(x/2)/cos(x/2)
= 2 sin(x/2) cos³(x/2)
2sin A cos B = sin2A
Use the above trigonometric identity and after simplification we get:
= (1+cos(x))(sin(x))
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Thus, the trigonometric expression (1+cos(x))2(tan(x/2)) is equivalent to (1+cos(x))(sin(x)) option (d) is correct.
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