Question

tan^-1[(√1+x)-(√1-x)/(√1+x)+(√1+x)]=π/4-1/2जहा -1/2≤x≤1​

Answer 1

MATHS

The number of values of x∈[0,4π] satisfying

∣

∣

∣

3

cosx−sinx

∣

∣

∣

≥2 is

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ANSWER

given, ∣

3

cosx−sinx∣≥2

⇒∣cos

6

π

cosx−cos

6

π

sinx∣≥1

⇒∣cos(x+

6

π

)∣≥1

but we know ∣cos(x+

6

π

)∣≤1

Hence,

⇒∣cos(x+

6

π

)∣=1⇒cos(x+

6

π

)=±1

Hence solutions in the given interval are,

x=

4

3π

,

4

7π

,

4

11π

,

4

15π