71 Consider the following statements 1 There exists at least one value of x between 0 and and pi 2 w...........

Quantitative Aptitude (CDS) Trignometry

71. Consider the following statements:

1. There exists at least one value of x between 0 and and π/2 which satisfies the equation sin⁴ x - 2sin² x - 1= 0.

2. sin 1.5 is greater than cos 1.5.

Which of the above statements is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

sin⁴x−2sin²x−1=0
⇒sin²x= (2±√8)/2 =(2±2√2)/2 =1±√2
But, 0≤sin²x≤1
Now 1+√2>0 and 1−√2<0
So, there exists no value of x between 0 and $\pi$ /2

which satisfies the given equation. Hence, statement (1) is incorrect

1.5 radian ≈ 86°
sin 86° > cos 86°
Hence, statement (2) is correct

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