Archives

Integrate ∫ (√tanx + √cotx) dx

We have to determine the integral of ∫ (√tanx + √cotx) dx Let us assume that I = ∫ (√tanx + √cotx) dx We know that tan and cot can be... View Article

Find the integral of (sinx-cosx)/(1+sinxcosx) with limits zero to pi/2.

On changing x= , On adding both the integrals, =>2I =0 => I=0 Check out the video given below to know more about trigonometry... View Article

Integrate (1/1+cotx) using substitution method.

Let I= We will solve the equation by substitution method. In this method of integration by substitution, any given integral is transformed... View Article

Integrate [sinx] / (2+sin 2x).

⇒ ⇒ Now put sinx - cosx = t, then [cosx + sinx]dx = dt and put sinx + cosx = u, then [sinx-cosx]dx = du ⇒ ⇒ ⇒ Check out the... View Article

Integrate [x-sin x] / [1- cos x].

The given equation is [latex] \int \frac{x-\sin x}{1-\cos x} dx[\latex] [latex] \int \frac{x-\sin x}{1-\cos x}[\latex] On using double angle... View Article

Find the integral of xlogx/(1+x²)² under the limits 0 to infinity.

Answer: . . . Apply Integration By Parts . . ⇒ . . On computing the boundaries, = 0 - 0 = 0... View Article

Prove that cos 20 degree * cos 40 degree * cos 80 degree =1/8.

cos20 cos40 cos80 multiply and divide by 21/2 (2 cos20 cos40 cos80)1/2 (cos(20+80)+ cos(20-80)) cos40 (2cosa cosb= cos(a+b) + cos(a-b))1/2... View Article

If sin^–1x +sin^–1y =π/2 , then find the value (x+y)^2.

The range of sin–1x is [-pi/2, pi/2]. Given that sin^-1x +sin^-1y = π Each of sin-1x, sin-1x takes value of pi/2. So, x = 1, y = 1... View Article

Prove that: (sec8A – 1) / (sec4A – 1) = tan8A/tan2A.

Proof Consider the LHS (sec 8A -1) / (sec 4A -1) => [(1 - cos 8A)/ cos 8A] / [(1 - cos 4A)/ cos 4A] => [2 sin² 4A / 2 sin² 2A] * [cos... View Article

If sinA – sinB = c and cosA – cosB = d then find cosec^2 [(A + B)/2].

Sin(A) - sin( B) = 2 sin ( A-B /2) cos (A +B/2) = c....(1)Cos(A)- cos(B)= 2 sin ( B - A/2)sin ( A+B/2)= d....(2)Dividing equation 1 and 2Cot (... View Article

Prove that tanA/secA+1 +cotA/cosecA+1= cosecA+secA-secAtanA.

Given that LHS = [tanA/secA+1] + [cotaA/cosecA+1] = tan A(sec.A — 1)/(sec A+1)(sec A—1) + cot.A(cosec.A — 1)/(cosec A+1)(cosecA — 1) =... View Article

If sin 2a + sin 2b = 1/2 and cos 2a + cos2b = 3/2, then cos²(a-b) is equal to(A) 3/8(B) 5/8 (C) ¾(D) 5/4

Given sin 2a + sin 2b = 1/2 cos 2a + cos2b = 3/2 Find out We have to determine the value of cos2(a-b) Solution We know the identity sin... View Article

Show that cos(6x)=32cos^6(x)-48cos^4(x)+18cos^2(x) -1

We have to prove cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1 Consider the L.H.S. = cos 6x cos 6x can be expressed as = cos 3(2x) We know... View Article

What is the value of cos(180)?

Answer: The value of cos 180 is equal to -1 The value of cos 180 degrees or the value of cos pi can be represented in terms of different angles... View Article

Prove that cosA+cosB+cosC is always positive in triangle ABC.

LHS = cosA+cosB+cosC.. = ( cos A + cos B ) + cos C = { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C = { 2 ·... View Article

Find the value of tan1.tan2.tan3…………………..tan89.

We need to find the value of tan 1° tan 2° tan 3° … tan 89° tan 1° tan 2° tan 3° … tan 89° = [tan 1° tan 2° … tan 44°] tan 45°[tan (90° –... View Article

If sinA+sinB+sinC+sinD=4 then find sinA.sinB.sinC.sinD.

Given sinA+sinB+sinC+sinD=4 Find out We have to determine the value of The range of sine function is 0<=x<=1. Sine Function Range... View Article

If secθ = x + 1/4x, then prove that, secθ + tanθ = 2x or 1/2x.

Given that secθ = x+1/4x 1+ tan²θ = sec²θ or tan²θ = sec²θ - 1 on expanding tan²θ = ( x+1/4x)² -1 or... View Article

Find the value of tan(-135) and cot(-135) along with the steps.

We have to determine the value of tan(-135) and cot(-135) tan(-135) tan(-135) can be expressed as tan (-135º) = tan (360º - 135º) = tan... View Article

If sin^-1 x + sin^-1y + sin^-1 z = π, then prove that x√1 – x² + y√1 – y² + z√1 – z² = 2xyz

Given equation sin-1 x + sin-1 y + sin-1 z = π To prove We have to prove x√1 - x2 + y√1 - y2 + z√1 - z2 = 2xyz Let us assume that , sin-1 x... View Article

M	T	W	T	F	S	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31