IT using the fact that 12 sin 12 3 4 ||

Q: tan? x sec² x + secx Prove -cos x

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Q: tanx)-sinx) lis sintx) 1/2. -5/4 O 7/2 o 5/4 O

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Q: Verify the identity tanh2 x + sech2 x = 1

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Q: - sin ( 7 ) 2 What is the exact value of

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Q: 2In(sin) de tan() 02

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Q: Q2. Prove that sec2(tan-x) = 1+ x?

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Q: Expand and simplify: sin(x+3)-cos(+ x) 6 COS X

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Q: If f(x) = 7 sin-(*), then f'(2) - =

A: dsin-1xdx = 11-x2 dxndx=n.xn-1

Q: Evaluate using substitution.

A: Evaluate the value of limit using substitution. Substitute the value for x and find out the limit.…

Q: Suppose that sin(θ)=4/8. What tan(θ)=______.

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Q: 16. tan²(x) + sec²(x) = 1 O True O False

A: Consider a right angled triangle.

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5)| (3220° – sin 20 + jln5)*|

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Q: Which expression is equal to sec⁡xsin⁡xcot⁡x+tan⁡x using identities? sin^2x cos^2x -cos^2x

A: As per your question no any option matched...but for x=0 one option is satisfying...and that option…

Q: 4. Evaluate tan²(x)dr. | tan

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Q: Evaluate: " sin' (;) 4 .2

A: Evaluate :     ∫0πsin7x2cos4x2dx

Q: tan 4 ;sin 3

A: We know, tan(π4)=1sin(π3)=32 Hence, tan(π4)=1;sin(π3)=32

Q: Evaluate the integral.

A: to evaluate I=∫π4π3tanθsin2θdθ

Q: tan (2 sin –1 )|

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Q: Prove that X +. 8 2 1 sin x X sin 8 2 sin %3D

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Q: 2 tan 79. Sin x = 1+ tan

A: We need to prove: sin x = 2 tan x21+tan2 x2 This can be proved as follows:

Q: 13) sin- 15) tan--1 1/-

A:

Q: 11. sin(2 tan-1 (-) 3,

A: A trigonometric ratios sin, cos, tan can take the input in the unit of degree or radians. The…

Q: 3. Rewrite the expression tan (2x) sec² (2x) entirely in terms of tangent.

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Q: sec(2) tan(2) – 1 dz 3.

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Q: What is the range of 3 sin(4x + II)+ 2 ? O -3, 2] O (-3, 3] O -1, 5] O (-1, 3]

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Q: How does ±√((csc^2x-1)/(csc^2x)) equal on of these: secx, cosx, sinx, tanx, cotx, cosx, or 1

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Q: Prove that X X sin 8 2 sin sin x 8 2,

A: The objective of the problem is to prove the equation. sin2π8+x2-sin2π8-x2=12sinx

Q: Using the result of the previous question, explain why 1 n sin" xdx = - sin"-2 xdx. n and hence show…

A: The given problem is to show the result of given integral with using the given integral result.

Q: provethat 2. 1- cosx +Sin'x

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Q: (B) Evaluate | tan (7x +1) sec³(7x +1) dr.

A: We will use simple integration rules to solve this question.

Q: 5. 4 f sin + 2zdz

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Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5) (320° – sin 20 + jln5)*

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Q: Explain why sin-1 3 is not defned.

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Q: If f(x) 5 tan (7 sin(2r)), f'(x) =

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Q: 7. tan (8x) sec (8r) da

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Q: If f(æ) = 8 sin-(*), then f (2) =

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Q: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Q: Derive/Prove: sin 2x = 2 sin x cos x

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Q: Prove sin 2  x/2=  tan x - sin x / 2 tan  x

A: The given identity is sin2x2=tanx-sinx2tanx

Q: If secA=x+1/4x ,prove that secA+tanA=2x or 1/2x

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Q: 2. sec x 4 tan<x + 7 tan x + 12

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Q: Determine 1-/[e-tt sin(2t)] 2- 23+3s)*

A: Given

Q: Let x = 5 sin 8, π/2 < 0 < π/2. Simplify the express X √ 25 - x² X √ 25-x² X

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Q: tan(sin^−1(3/4))

A: The objective is to find the required value

Q: Prove that X -sin 8 2 X sin sin x 8 2 2. 2.

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Q: 3. Rewrite the expression tan (2x) sec²(2x) entirely in terms of tangent.

A: Given: tan52xsec22x Formula Used: sec2x+tan2x=1

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.