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Prove
Consider,
Prove
L.H.S =
Prove
test
Prove
Now, we have:
Prove
Using (1) and (2), we have
Solveis equal to
(A) (B) (C) (D)
Solveis equal to
(A) (B). (C) (D)
Hence, the correct answer is C.
Find the value of
We know that cos−1 (cos x) = x if, which is the principal value branch of cos −1x.
Here,
Now, can be written as:
Find the value of
We know that tan−1 (tan x) = x if, which is the principal value branch of tan −1x.
Here,
Now, can be written as:
Prove
Now, we have:
Prove
Now, we have:
Prove
Now, we will prove that:
Prove
Let Then,
Prove [Hint: putx = cos 2θ]
Put so that , then we have
Solve
Solve
Solve, then x is equal to
(A) (B) (C) 0 (D)
Therefore, from equation (1), we have
Put x = sin y. Then, we have:
But, when, it can be observed that:
is not the solution of the given equation.
Thus, x = 0.
Hence, the correct answer is C.
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