# Find the exact value of trigonometric function sec2x if sinx =3/5, cosx=4/5Find the exact value of trigonometric function sec2x if sinx =3/5, cosx=4/5

justaguide | College Teacher | (Level 2) Distinguished Educator

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To find the value of sec (2x) if sin x = 3/5, cos x = 4/5, use the relation sin 2x = 2*sin x * cos x and (cos x)^2 = 1 - (sin x)^2

sin 2x = 2*sin x * cos x = 2*3/5 * 4/5

=> sin 2x = 24/25

(cos 2x)^2 = 1 - (sin 2x)^2 = 1 - (24/25)^2 = 49/625

cos 2x = -7/25 and 7/25

sec 2x = 1/ cos 2x = 25/7 and -25/7

The values of sec 2x are (-25/7, 25/7)

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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Since sec 2x = 1/cos 2x, we'll compute the value of cos 2x, given the values of sin x and cos x.

We'll apply double angle identity:

cos 2x = cos x*cos x - sin x*sin x

cos 2x = (cos x)^2 - (sin x)^2

We'll replace cos x and sin x by the given values:

sinx =3/5 and cosx=4/5

cos 2x = (4/5)^2 - (3/5)^2

cos 2x = 16/25 - 9/25

cos 2x = 7/25

We'll replace the value of cos 2x in sec 2x identity:

sec 2x = 1/(7/25)

The requested exact value of sec 2x = 25/7.