Question

tan thita =5÷12 and thita is acute angle then the value of sec thita + cosec thita

Answer 1

secθ+tanθ=221/60 is answer

Answer 2

hello users ...

solution:-
we know that:
sec x = √ ( 1 + tan² x)

And
cosec x = √(1 + cot²x)

Here,
tan θ = 5 /12 

And
sec θ = √ ( 1 + (5/12)² ) 
= √ ( 1 + 25 / 144) 
= √ { (144 + 25) / 144}   ...taking LCM ...
= √ 169/144
= √ 13² / 12²
= 13 / 12

And
cot θ = 1 / tanθ = 12 / 5 

Here,
cosec θ = √ ( 1 + (12/5)² 
= √ ( 1 + 144/25)
= √ { ( 25 + 144) / 25} .. taking LCM ...
= √ (169 / 25 )
= √ 13² / 5² 
= 13 / 5 

Now,
sec θ + cosec θ = 13 / 12 + 13 / 5

= (13 * 5 + 13 * 12 ) / 60 

= ( 65  + 156) / 60 

= 221 / 60 Answer 

# hope it helps :)