If tan A -1-cos B -sin B- then find the value of tan 2 A-

Given: tan A =1 cos B/sin B=2 sin^2 B/2/2 sin B/2 cos B/2=tan B/2 tan 2A =2 tan A/1 tan^2 A Subtitute the value of tan A, we get, tan 2A =2 tan B/2/1 tan^2 B/2 ...

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Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

If tan A =1-c...

Question

If $t a n A = \frac{1 - c o s B}{s i n B}$ , then find the value of tan 2A.

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Solution

Given:

$t a n A = \frac{1 - c o s B}{s i n B} = \frac{2 s i n^{2} \frac{B}{2}}{2 s i n \frac{B}{2} c o s \frac{B}{2}} = t a n \frac{B}{2} t a n 2 A = \frac{2 t a n A}{1 - t a n^{2} A}$

Subtitute the value of tan A, we get,

$t a n 2 A = \frac{2 t a n \frac{B}{2}}{1 - t a n^{2} \frac{B}{2}} = t a n B$

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If tan A=1−cos Bsin B, then find the value of tan 2A.

Given: tan A=1−cos Bsin B=2 sin2 B22 sin B2 cos B2=tan B2tan 2A=2 tan A1−tan2 A Subtitute the value of tan A, we get, tan 2A=2 tan B21−tan2 B2=tan B

If $t a n A = \frac{1 - c o s B}{s i n B}$ , then find the value of tan 2A.