Question

if cosA=7/25 Find the value of tanA + cotA​

Answer 1

cosA=7/25

cos theta =b/h

so 7/25= b/h

applying phythagoras theorem

h^2=b^2+p^2

25^2=7^2+p^2

625-49=p^2

576=p^2

p=√576

p=24

tanA=p/b , cotA=b/p

tanA=24/7 ,cotA=7/24

now, 24/7+7/24

576+49

--------------

168

625

-------

168

Answer 2

${\underline{\bold{Answer}}}$→$\frac{625}{168}$

${\bold{\underline{Step\:by\:Step\:Explanation}}}$→

$= > Cos A = \frac{7}{25}$

We know that :

$Cos \: \theta = \frac{Base \: (B)}{Hypotenuse \: (H) }$

→ Use the Pythagoras Theorem to find the third side of the triangle :

➡ (H)² = (B)² + (P)²

=> (25)² = (7)² + (P)²

=> 625 = 49 + P²

=> P² = 625 - 49

=> P² = 576

$= > P = \sqrt{576}$

${ \bold{P = 24 \: cm \: }}$

Now ,

$Tan A \: = \frac{Prependicular \: ( P) }{base \:(B)}$

$= >{ \bold{ Tan A = \frac{24}{7} }}$

Also ,

$Cot A = \frac{1}{Tan \: A}$

$= > { \bold{Cot \: A = \frac{7}{24} }}$

♦Plug the values of Cot A and Tan A in the given equation ,

$→ Tan A + Cot A \: = \frac{7}{24} + \frac{24}{7} \\ \\ → \frac{49 + 576}{168} \\ \\ → \frac{625}{168}$

Hence we have ,

${ \bold { \boxed {Tan \: A \: + Cot \: A \: = \frac{625}{168} }}} = 3.72 \:( approx.)$