Q65 of 76 Page 52

Fill in the blanks

3(sin x – cos x)4 + 6 (sin x + cos x)2 + 4(sin6 x + cos6 x) = _______.

We have, 3(sin x – cos x)4 + 6 (sin x + cos x)2 + 4(sin6 x + cos6 x)


=3(sin2x+cos2x-2sin x cos x)2+6(sin2x+cos2x+2sin x cos x) +4[(sin2x)3 + (cos2x)3]


=3(1-2sin x cos x)2+6(1+2sin x cos x) +4[(sin2x+ cos2x)3 -3 sin2x cos2x(sin2x+ cos2x)]


=3(1+4 sin2x cos2x-4sin x cos x) +6+12sin x cos x+4-12sin2x cos2x


=3+12 sin2x cos2x-12 sin x cos x+6+12sin x cos x+4-12sin2x cos2x


=3+6+4


= 13


More from this chapter

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63

Fill in the blanks

If sin x + cos x = a, then


(i) sin6 x + cos6x = _______


(ii) |sin x – cos x| = ______.

 64

Fill in the blanks

In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ________.


[Hint: A + B = 90°⇒ tan A tan B = 1 and tan A + tan B ]

 66

Fill in the blanks

Given x > 0, the values of lie in the interval _______.

 67

Fill in the blanks

The maximum distance of a point on the graph of the function from x-axis is _____.