"Please see proof below." # "One way we can do this by converting to sines and cosines:" \\ ( tan^2 x + 1 ) ( cos^2x - 1 ) \\qquad \\qquad \\qquad \\qquad = \\ tan^2 ...

Recall that secx= 1/cosx. Therefore 1 - (1/cosx)cos^3x= sin^2x 1 - cos^2x = sin^2x And since sin^2x + cos^2x =1, then sin^2x = 1- cos^2x. sin^2x= sin^2x LHS = RHS Hopefully this helps!

How do you use the sum and difference formula to simplify sec 1275? Trigonometry Trigonometric Identities and Equations Sum and Difference Identities

Equation of normal line is x+ 1.17y =0.87 x=pi/8 ~~0.39 ; f (x)=tanx = or f (x)= tan (pi/8) ~~ 0.41 So at (0.39,0.41) tangent and normal is drawn. Slope of the tangent is f' (x)= sec^2x. at x=pi/8 …

How do you express #f (theta)=4sin^2 (theta)-6sec^2 (theta)-cot^4theta# in terms of non-exponential trigonometric functions?

Now we use the sine and cosine sum of multiple angle identities:

Proofs below a) We first use the facts that sinu/cosu = tanu and cos^2u+sin^2u =1: (1+tan^2u) (1-sin^2u) = (1+sin^2u/cos^2u) (cos^2u) Expand: = (cos^2u+sin^2u) And done: =1 b) We need to …

How do you verify # (1 + sec^2 x) / (1 + tan^2 x) = 1 + cos^2 x#? How do you find the derivative of #ln ( (x+1)/ (x-1))#? What is a particular solution to the differential equation # (du)/dt= …

Feb 18, 2018 · Verify these identities? sin^2x-tan^2x = -sin^2xtan^2x 1/ (secx-tanx) = tanx+secx

Apr 11, 2018 · Let 2y =x. Then the identity becomes tan (y) = sec (2y)/ (sec (2y)csc (2y) + csc (2y)) tany = (1/cos (2y))/ (1/ (cos (2y)sin (2y)) + 1/sin (2y)) tany = (1/cos (2y ...