Q. Prove that : tan20 + 4sin20 = root 3
S.E.E. Solution
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Soln: L.H.S. = tan20 + 4sin20 = sin20/cos20 + 4sin20 = (sin20 + 4sin20.cos20)/(cos20) = (sin20 + 2sin40)/cos20 = [sin20 + 2sin...
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Q. Prove that: cos(theta)-sqrt(1+sin2(theta))/sin(theta)-sqrt(1+sin2(theta) = tan(theta)
Soln:
... Q. h(x) = x/(2-x) and g(x) = ax-5 are two functions. IF goh(4) = -13, find the values of 'a' and g-1(1).
Soln:
h(x) = x/(2-x)
So, h(4) = 4/(2-4) = -2
We have, goh(4) = -13
or, g[h(4)] = -13
or, g(-2) = -13 ... Q. The inverse of the function f(x)=ax+b, x∈R is f-1(x)=8x-3.
Soln:
Here, f(x) = ax + b
Let y be the image of x under f, then
y = ax + b
x = (y-b)/a
Interchanging the role of x and y ... Q. If f(x) = x^2 – 2x, g(x) = 2x + 3 and fg-1(x) = 3 then find the value of x.
Soln:
To find g-1(x),
Let y be the image of x under g, then
y = 2x + 3
x = (y – 3)/2
Interchanging the role of x and y, we ha ... Q. Find the angle between the lines represented by the equation (x^2 + y^2)sin^2a = (xcosa – ysina)^2.
Soln:
(x^2 + y^2)sin2a = (xcosa – ysina)^2
x2sin2a + y2sin2a
= x2cos2a – 2xycosa.sina + y2sin2a
(sin2a – cos2a)x2
+ 2x ... A complete solution for SEE students.
