819. Ifsec O â tan 0 = 4, then prove that cos 0= â" .

1.	819. Ifsec O â tan 0 = 4, then prove that cos 0= â" .
Answer» secθ - tanθ = 4 -----> (1) Multiplying and dividing bysecθ +tanθ =secθ - tanθ×secθ +tanθ/secθ +tanθ = sec²θ - tan²θ/secθ + tanθ = 4 we know that --> sec²θ - tan²θ = 1 1/secθ + tanθ = 4 therefore , secθ + tanθ = 1/4----> (2) Adding equations (1) and (2) :- secθ - tanθ = 4 secθ + tanθ = 1/4 --------------------------2secθ = 4 + 1/42secθ = 17/4 secθ = 17/4*2 = 17/8 we know that cosθ = 1/secθ = 1/(17/8) = 8/17

Answer»

secθ - tanθ = 4 -----> (1)

Multiplying and dividing bysecθ +tanθ

=secθ - tanθ×secθ +tanθ/secθ +tanθ

= sec²θ - tan²θ/secθ + tanθ = 4

we know that --> sec²θ - tan²θ = 1

1/secθ + tanθ = 4

therefore ,

secθ + tanθ = 1/4----> (2)

Adding equations (1) and (2) :-

secθ - tanθ = 4

secθ + tanθ = 1/4 --------------------------2secθ = 4 + 1/42secθ = 17/4

secθ = 17/4*2 = 17/8

we know that

cosθ = 1/secθ = 1/(17/8) = 8/17

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