Question

please solve this question​

Answer 1

Given :-

secθ  -tanθ  = 1/3

To find :-

secθ  + tanθ  

Solution :-

As we know from trigonometric identities ,

sec²θ  -tan²θ  = 1

As we know that

(a + b) (a- b ) = a² - b²

So,

(secθ  + tanθ  )(secθ -tanθ ) =1

As we need to find the secθ +tanθ  from this,

secθ  + tanθ  = 1/ (secθ  -tanθ )

secθ  + tan θ = 1/(1/3)

secθ  + tan θ  = 3

So, the correct option is option - c

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Know more :-

Trigonometric Identities:-

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigonometric relations:-

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonometric ratios:-

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj

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csc²θ - cot²θ = 1

(cscθ + cotθ)(cscθ-cotθ) = 1

cscθ+ cotθ = 1/(cscθ-cotθ)

cscθ- cotθ = 1/(cscθ+ cotθ)

sec²θ - tan²θ = 1

(secθ+tanθ)(secθ-tanθ) =1

secθ+ tanθ = 1/(secθ-tanθ)

secθ-tanθ = 1/(secθ+tanθ)