if cos y=x cos (a+y), (a!= 0) , then sho...

if cos y=x cos (a+y), `(a!= 0)` , then show that `dy/dx= cos ^2(a+y)/sin a`

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HIGHER SECONDARY QUESTION 2018
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If cosy=xcos(a+y),(ane0) , then show that (dy)/(dx)=(cos^2(a+y))/(sina) .

If cosy=x cos(a+y)," prove that " (dy)/(dx) =(cos^(2)(a+y))/(sin a) , where a ne 0 is a constant .

If (cos x)^y = (cos y)^x then show that (dy)/(dx) = (y tan x+log cos y)/(x tan y+log cos x).

If cos y= x cos (a+y) , with cos a ne pm 1 , prove that (dy)/(dx)=(cos^(2)(a+y))/(sin a) .

If xsin^3a+ycos^3a = sin a cos a and x sin a- y cos a = 0 , then show that x^2+y^2= 1 .

If x= cos theta+ I sin theta and y= cos psi + I sin psi , then show that (x)/(y)+(y)/(x)= 2 cos (theta- psi) .

If x^2 = a^(sin^(-1)t) and y^2= a^(cos^(-1)t) then show that (dy)/(dx)=-y/x .

If cosx + cosy + cosz = 0 "and" sinx + siny + sinz =0, "then show that" cos (x-y) + cos(y - z) + cos(z - x) = - 3/2.

If y = a cos(logx) + b sin(log x) , show that, x^2(d^2y)/(dx^2)+x(dy)/(dx) + y = 0

If y=cos(2sin^(-1)x) , then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+4y=0

UNITED BOOK HOUSE-HIGHER SECONDARY QUESTION 2019-EXERCISE

show that A(2,3,-4),B (1,-2,3) and C(3,8,-11) are collinear.
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if vec a= 5 hat i -hat j -3 hat k and vec b=hat i+3 hat j - 5 hat k , ...
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(e)ANSWER ANY one question : 1. if P(A) =a and P(B)=b, then show that ...
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if a and b are any two constants, then prove that Var (aX+b)=a^2Var(X)...
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if tan ^(-1) x+tan ^(-1)y+tan ^(-1) z=pi/2 and x+y+z= sqrt3 , then sho...
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(b) answer the following questions: 1. if A=[[1,2,2],[2,1,2],[2,2,1]],...
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if AB=[[i,-i],[-i,i]] and B=[[1,-1],[-1,1]], then show that A^8=128B
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Answer the foll. Question : 2.show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]...
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if cos y=x cos (a+y), (a!= 0) , then show that dy/dx= cos ^2(a+y)/sin ...
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answer the foll. Questions 2. evaluate : int sqrt(1+sec x dx).
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or, evaluate : int dx/((x-1)+ sqrt(x^2-1)
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answer the foll. Questions 3. solve :(e^x+1)y dy-(y^2+1) e^x dx=0 , gi...
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(d) answer ANY one question :1. bar a, bar b and bar c be three vector...
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answer any one question 2. if sum of two unit vectors be a unit vector...
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(e)answer any one question : 1. using integral calculus , find the are...
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answer any one question 2. prove that int1^3 dx/(x^2(x+1))=2/3+ log (2...
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answer any one question : 2.eight unbiased coins tossed . Find the pro...
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answer any two questions :2.solve (1+x^2)dy+2xy dx=cot x dx.
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answer any two questions 4. evaluate : lim (n rarr infty) [n/(n^2+1^2)...
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