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प्रश्न
If cos A = `(2x)/(1 + x^2)`, then find the values of sin A and tan A in terms of x
उत्तर
cos A = `(2x)/(1 + x^2)`
In the triangle ABC
BC2 = AC2 – AB2
= (1 + x2)2 – (2x)2
= 1 + x4 + 2x2 – 4x2
= x4 – 2x2 + 1
= (x2 – 1)2 or (1 – x2)2 ...[using (a – b)2]
BC = `sqrt((x^2 - 1)^2` or `sqrt((1 - x^2)^2`
BC = x2 – 1
The value of sin A = `"BC"/"AC" = (x^2 - 1)/(x^2 + 1)`
tan A = `"BC"/"AB" = (x^2 - 1)/(2x)`
and
BC = 1 – x2
The value of sin A = `(1 - x^2)/(x^2 + 1)`
tan A = `(1 - x^2)/(2x)`
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