Question

Number of solutions of the equation
cosx = 1 + sin⁴x
in interval [-20π , 40π] is

plz answer fast it's very urgent.
​

Answer 1

Answer:

cosx=

1−sin2x

=∣sinx−cosx∣

(a) sinx<cosx⇒x∈[0,

4

π

)∪(

4

5π

,2π]

Then the given equation is cosx=cosx−sinx

sinx=0⇒x=0,π,2π[fromequ.(i)]

x=π is not possible

(b) sinx≥cosx⇒x∈[

4

π

,

4

5π

]

cosx=sinx−cosx

tanx=2

x=tan

−1

2

Hence, there are three solutions.