Question

If sec 0=25/7,find the value of tan0.

Answer 1

Step-by-step explanation:

1+ tan^2 theta =sec^2 theta

tan^2 theta =[(25\7)^2 ]-1

= [625\49]-1

=[(625-49)\49

tan^2 theta = 576\49

tan theta =24 \7

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Answer 2

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{\:\:\:\:\:\:\:\: Given:-\:\:\:\:\:\:\:\:}}$

$\sf\:\: \bullet sec\theta=\dfrac{25}{7}$

• we have to find the value of

• $\sf tan\theta$

Now by formula

$\boxed{\sf{\purple{1+tan{}^{2}\theta=sec{}^{2}\theta}}}$

$\bf\underline{\red{\:\:\:\:\:\:\:\: A.T.Q:-\:\:\:\:\:\:\:\:}}$

$\sf\implies 1+tan{}^{2}\theta=\bigg(\dfrac{25}{7}\bigg){}^{2}\\ \\ \sf:\implies 1+tan{}^{2}\theta=\dfrac{625}{49}\\ \\ \sf:\implies tan{}^{2}\theta=\dfrac{625}{49}-1\\ \\ \sf:\implies tan{}^{2}\theta=\dfrac{625-49}{49}\\ \\ \sf:\implies tan{}^{2}\theta=\dfrac{576}{49}\\ \\ \sf:\implies tan\theta=\sqrt{\dfrac{576}{49}}\\ \\ \sf:\implies tan\theta= \dfrac{24}{7}$

$\boxed{\sf{tan\theta=\dfrac{24}{7}}}$