Question

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

Answer 1

hello users ...

solution:-
Given that :
cos A = 7 /  25 

we know that ;
sin x = √ (1 - cos²x)
And
tan x = sin x / cos x 
And
cot x = cos x / sin x  or 1 / tan x 

Here,
sin A =√ ( 1 - cos²A)
= √ { 1 - (7/25)² }
= √ ( 1 - 49/625)
= √ { ( 625 - 49 ) / 625 }     ... taking LCM ... 
= √ 576 / 625 
= √ ( 24/25)²
= 24 /25 

And
tan A = sin A / cos A
= (24/25 ) / ( 7/25 )
= 24 / 7 

And
cot A = 1/ tan A 
= 1/ ( 24/7) = 7/24 

now,
tan A + cot A = 24 / 7 + 7 / 24 
=  ( 576 + 49 ) / 168    ....taking LCM ...
 = 625 / 168  Answer 

# hope it helps :)

Answer 2

Hope it helps you !