Question

If sin teta =a/b find sec teta +tan teta in terms of a and b

Answer 1

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Answer 2

hello users .....

we have 
sin ∅ = a/b

we have to find 
sec ∅ + tan ∅ = ? in terms of a and b 

solution:-
we know that 
sec x = $\frac{1}{ \sqrt{1- sin^{2}x } }$
and 
tan x = sin x /cos x = sin x ×sec x

here 
sec ∅ = 1 / √{ 1 - (a/b)² }  =$\frac{b}{ \sqrt{ b^{2} - a^{2} } }$

and 
tan ∅ = sin ∅ × sec ∅ = $\frac{a}{b}$ × $\frac{b}{ \sqrt{ b^{2} - a^{2} } }$

= $\frac{a}{ \sqrt{ b^{2} - a^{2} } }$

=> sec ∅ + tan ∅ = $\frac{b}{ \sqrt{ b^{2} - a^{2} } }$ + $\frac{a}{ \sqrt{ b^{2} - a^{2} } }$

= $\frac{a + b}{ \sqrt{ b^{2} - a^{2} } }$

= $\frac{ \sqrt{a + b } * \sqrt{a+b} }{ \sqrt{a-b} * \sqrt{a+b} }$

= $\frac{ \sqrt{a +b } }{ \sqrt{a - b} }$ answer 


✪✪ hope it helps ✪✪