Q. 8cos^3(20) - 8sin^3(10) - 6cos20 + 6sin10 = 2
S.E.E. Solution
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Soln: L.H.S. = 8cos 3 20 – 8sin 3 10 – 6cos20 + 6sin10 = 2(4cos 3 20 – 4sinn 3 10 – 3cos20 + 3sin10) = 2(4cos 3 20 - 3cos20 +...
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11. Find the number of geometric means inserted between 1 and 243 in which the ratio of the first mean to the last mean is 1:27.
Soln:
... 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. If 2Tanα = 3Tanβ, then show that Tan(α-β) = Sin2β/(5-Cos2β)
Soln:
2tanα=3tanβ
tanα=(3/2)tanβ
L.H.S.
= tan(α-β)
= (tanα-tanβ)/(1+tanα.tanβ)
= {(3/2)tanβ-tanβ}/{1+(3/2)tanβ.tanβ}
= ... 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. Prove that: 4(cos^4A+sin^4A)/(cos^4A-sin^4A)=(3+cos4A)Sec2A
... A complete solution for SEE students.
