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If θ is an acute angle, then find sin(π4-θ2), when sin θ = 125

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प्रश्न

If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`

बेरीज
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उत्तर

`sin (pi/4 - theta/2)`, when sin θ = `1/25`

`sin (pi/4 - theta/2) = sqrt((1 - cos2(pi/4 - theta/2))/2`

= `sqrt((1  cos(pi/2 - theta))/2`

= `sqrt((1 - sin theta)/2`

= `sqrt((1 - 1/25)/2`

= `sqrt((25 - 1)/50`

= `sqrt(24/50)`

= `sqrt(12/25)`

= `sqrt((4 xx 3)/(5 xx 5)`

= `(2sqrt(3))/5`

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Trigonometric Functions and Their Properties
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometry - Exercise 3.5 [पृष्ठ ११८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 3 Trigonometry
Exercise 3.5 | Q 2. (i) | पृष्ठ ११८

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