Question

(ii)
1 - cos 2x/
1 + cos 2x
= tan square x​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

true

Step-by-step explanation:

• Verify the following identity:

(1 - cos(2 x))/(cos(2 x) + 1) = tan(x)^2

• Multiply both sides by cos(2 x) + 1:

1 - cos(2 x) = tan(x)^2 (cos(2 x) + 1)

• Write tangent as sine/cosine:

1 - cos(2 x) = (sin(x)/cos(x))^2 (cos(2 x) + 1)

• (cos(2 x) + 1) (sin(x)/cos(x))^2 = ((cos(2 x) + 1) sin(x)^2)/(cos(x)^2):

1 - cos(2 x) = (sin(x)^2 (cos(2 x) + 1))/(cos(x)

• Multiply both sides by cos(x)^2:

cos(x)^2 (1 - cos(2 x)) = sin(x)^2 (cos(2 x) + 1)

• cos(x)^2 = 1/2 (cos(2 x) + 1):

(cos(2 x) + 1)/2 (1 - cos(2 x)) = sin(x)^2 (cos(2 x) + 1)

• sin(x)^2 = 1/2 (1 - cos(2 x)):

((1 - cos(2 x)) (cos(2 x) + 1))/2 = (1 - cos(2 x))/2 (cos(2 x) + 1)

• The left hand side and right hand side are identical:

Answer: identity has been verified