For 0 ≤ P, Q ≤ π2, if sinP + cosQ = 2, then the value of tanP + Q2 is equal to
1
12
32
The value of
cos275° + cos245° + cos215° - cos230° - cos260° is
0
14
The maximum and minimum values of cos6θ + sin6θ are respectively
1 and 14
1 and 0
2 and 0
1 and 12
Let fθ = 1 + sin2θ2 - sin2θ. Then, for all values of θ
fθ > 94
f(θ) < 2
fθ > 114
2 ≤ f(θ) ≤ 94
If P, Q and R are angles of an isosceles triangle and ∠P = π2, then the value of
cosP3 - isinP33 + cosQ + isinQcosR - isinR + cosP - isinPcosQ - isinQcosR - isinR
i
- i
- 1
If fx = sinx + 2cos2x, π4 ≤ x ≤ 3π4. Then, f attains its
minimum at x = π4
maximum at x = π2
minimum x = π2
mamum at x = sin-114
C.
Given,
fx = sinx + 2cos2x, π4 ≤ x ≤ 3π4∴ f'(x) = cosx - 4cosx . sinxand f''(x) = - sinx - 4cos2xFor maximum or minimum of f(x)Put f'(x) = 0⇒ cosx - 4cosx . cosx = 0⇒ cosx1 - 4cosx = 0⇒ cosx = 0 = cosπ2 and sinx ≠ 14∵ x ∈ π4, 3π4⇒ x = π2Now, f''π2 = - sinπ2 - 4cosπ = - 1 + 4 = 3 > 0 minimumSo, f(x) is minimum at x = π2and its minimum value is,fπ2 = sinπ2 + 2cos2π2 = 1 - 2 × 0 = 1
If sin2θ + 3cosθ = 2 then cos3θ + sec3θ is equal to
4
9
18
Which of the following real valued functions is/are not even functions?
fx = x3sinx
f(x) = x2 cosx
fx = exx3sinx
f(x) = x - [x], where [x] denotes the greatest integer less than or equal to x.
Number of solutions of the equation tan(x) + sec(x) = 2cos(x), x ∈ [0, π] is
2
3
If sin-1x + sin-1y + sin-1z = 3π2, then the value of x9 + y9 + z9 - 1x9y9z9 is equal to