# Class 12th Calculus

If y = e^x cosx, prove that dy/dx sqrt(2) e^x . cos(x+ pie/4)

1. 👍 0
2. 👎 0
3. 👁 262
1. The simple dy/dx = e^x(-sinx) + e^xcosx
= e^x(cosx - sinx)

RS = √2(e^x)(cos(x+π/4)
= √2(e^x)(cosxcosπ/4 - sinxsinπ/4)
= √2(e^x)(cosx(1/√2 - sinx(1/√2)
= e^x (cosx - sinx)

= the dy/dx from above

1. 👍 1
2. 👎 0

## Similar Questions

1. ### math

if cos(B-C)+cos(C-A)+cos(A-B)=-3/2 then prove that cosA+cosB+cosC=O and sinA+sinB+sinC=O after that prove that cos(B-C)=cos(C-A)=cos(A-B)=-1/2

2. ### maths

(Sin^3x-cos^3x)/(sinx-cosx) – cosx/sqrt(1+cot^2x)-2tanxcotx=-1 where x∈(0,2pi) general value of x.

3. ### Maths

If sec(x+y),sec(x),sec(x-y) are in A.P. then prove that cosx= +-√2 cos y/2 where cosx and cosy are not equals to 1,

4. ### math

prove that 2sinxcosx-cosx/1 -sinx+sin^2x-cos^2x=cotx

1. ### Pre-calculus

Prove the following identities. 1. 1+cosx/1-cosx = secx + 1/secx -1 2. (tanx + cotx)^2=sec^2x csc^2x 3. cos(x+y) cos(x-y)= cos^2x - sin^2y

2. ### Trig.......

I need to prove that the following is true. Thanks (2tanx /1-tan^x)+(1/2cos^2x-1)= (cosx+sinx)/(cosx - sinx) and thanks ........... check your typing. I tried 30º, the two sides are not equal, they differ by 1 oh , thank you Mr

3. ### Maths

Solve this equation fo rx in the interval 0

4. ### Pre-calculus

solve 4 sin^2x + 4 sqrt 2 cos x-6=0 for all real values of x. Going by the example in the book I got to: 4 cos^2x + 4sqrt2 cosx -10 = 0 but do not know how to proceed. Any help would be great. Thanks

1. ### Math

Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx I did some of these so far, don't know if it is correct. Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx

2. ### math

verify for sqrt(1-cosx)= sin/sqrt(1+cosx). I multiplied the right side by sqrt(1-cosx) and got sqrt(1-cosx)= sin*sqrt(1-cosx), but I don't know what to do with the sin.

3. ### Trigonometry

Simplify #1: cscx(sin^2x+cos^2xtanx)/sinx+cosx = cscx((1)tanx)/sinx+cosx = cscxtanx/sinx+cosx Is the correct answer cscxtanx/sinx+cosx? Simplify #2: sin2x/1+cos2X = ??? I'm stuck on this one. I don't know what I should do.

4. ### Calculus

Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help. Calculus - Steve, Tuesday, January 12, 2016 at