1. Given sinx 12 and cos y : 13 both x and y lie in sxs, determine a) cos(x+y) b) sin 2y

Q: 4. Establish the identity: sec ar - secr sin2 = cos LIC HS O6Y

A: Establish the identity

Q: s+2s ds s2+1

A: I have stated the used formulas in the solution.

Q: Evaluate [sin³ a x cos x dx. + C

A:

Q: 48. Simplify a. 1/cos x b. 1/secx c. 1/tan x d. 1/sin x 1 sin³ x col² x sin x

A:

Q: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.

A: 5.Solution…

Q: cos t 1-sin t sect + tant

A:

Q: 2. Estimate cos (– 0.1) + cos 4

A: As per given question  We have to solve above question

Q: Veridy that x - T -Ž ?I ti) e -n4 sin (nx) and 00 -n sin (nx) are equivalent .

A: The Fourier series expansion of x3-π2x in the interval -π to π is given by…

Q: If sin(x+y) - - sinx + 뜰 conx, what is the value of y? O 0 이용 6

A: Topic = Trigonometry

Q: 10. Prove that 7/2 sin 0 cos ! (cos a cosec 0) d0 /2- TC (1-cos a). COS

A:

Q: Compute / sin? æ dæ. sin 2x + C 4 sin a +C 3 cos 2x + C 4 2 sin 2x + C 4 cos 2x + C 4 2

A:

Q: snip

A:

Q: i) Simplify sin(2sin-1x). ii) Show that sin 30 = 3 sin 0 – 4sin30. iii) By using the substitution 0…

A:

Q: (b) Differentiate y cos-1 23

A: Differentiate the given y with respect to x.

Q: 2. Simplify: cos(+ x) cos(-x) = sin(n + x) sin(x + 37)

A:

Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: 6. Prove that: ah cos (i) A sin (ar + b) = 2 sin (ah sin a (ii) A cos (ar + b) = - 2 sin

A:

Q: Verify the identity : cos(α - β)/(cos α .sin β) = tan α + cot β

A: Given : cosα - βcosα sinβ = tanα + cotβ

Q: 1) 2) 1 sinx.cosx dx 4 + sin?x dx VX (1– X) (x – 1) X^

A:

Q: Prove:  cos(π   + x)        2             =−sinx     Please write clearly thank you.

A: We have to prove that cosπ2+x=−sinx. Use formula cosA+B=cosAcosB−sinAsinB Here, A=π2 and B=x Hence,…

Q: y = cosx sinx

A: Given query is to the derivative of the expression.

Q: 3. Express into standard form: = = 8[cos (-5) + + sin(-5)] Z i 3 3

A: Solution

Q: 4. If (sin2x + cos2x)dx =, sin(2x – c) + a, find the values of a and c.

A: Introduction :