Step 1: Correctly stated the double angle identity for cosine: cos(2x) = cos²(x) - sin²(x). Step 2: Here, you mentioned that sin²(x) should have been replaced with 1 + cos²(x). However, this is incorrect. The correct replacement for sin²(x) is 1 - cos²(x), not 1 + cos²(x). The correct step should be: The Cos (2x) Formula: The first identity for cos ( 2 x) is. cos ( 2 x) = cos 2 x − sin 2 x. This can be derived from the sum formula for cosine, which is shown below. cos ( α + β) = cos α cos Change to sines and cosines then simplify. #1+tan^2x=1+(sin^2x)/cos^2x# #=(cos^2x+sin^2x)/cos^2x# but #cos^2x+sin^2x=1#. we have #:.# #1+tan^2x=1/cos^2x=sec^2x # The derivative of 1/cos (x) is tan (x)sec (x). This can be found using the quotient rule, or through trigonometric identities, since 1/cos (x) = sec (x). The expression 1 + cos 2x + cos 4x + cos 6x is equivalent to. NCERT Solutions. NCERT Solutions For Class 12. NCERT Solutions For Class 12 Physics Recall the formula. cos(2θ) = 2cos2(θ) − 1 cos ( 2 θ) = 2 cos 2 ( θ) − 1. This gives us. cos2(θ) = 1 + cos(2θ) 2 cos 2 ( θ) = 1 + cos ( 2 θ) 2. Plug in θ = 2x θ = 2 x, to get what you want. EDIT The identity. cos(2θ) = 2cos2(θ) − 1 cos ( 2 θ) = 2 cos 2 ( θ) − 1. can be derived from. cos(A + B) = cos(A) cos(B) − sin(A .

what is 1 cos 2x