If sec-tan-45 and sec-tan-m- then the value of m-12 is equal to

Given : secθ tanθ=45...(i) and, secθ+tanθ=m...(ii) Multiplying (i) and (ii), we get (secθ tanθ)× (secθ+tanθ)=45× m ⇒ sec^2θ tan^2θ=4m5 ⇒ 1=4m5 (∵ 1+tan^2θ= ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identities

If secθ-tanθ=...

Question

If $s e c θ - t a n θ = \frac{4}{5} a n d s e c θ + t a n θ = m,$ then the value of $(m + 1)^{2}$ is equal to

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Solution

The correct option is A
Given : $s e c θ - t a n θ = \frac{4}{5} . . . (i) a n d, s e c θ + t a n θ = m . . . (i i) Multiplying (i) and (ii), we get (s e c θ - t a n θ) \times (s e c θ + t a n θ) = \frac{4}{5} \times m \Rightarrow s e c^{2} θ - t a n^{2} θ = \frac{4 m}{5} \Rightarrow 1 = \frac{4 m}{5} (∵ 1 + t a n^{2} θ = s e c^{2} θ) \Rightarrow m = \frac{5}{4} ∴ (m + 1)^{2} = {(\frac{5}{4} + 1)}^{2} = {(\frac{9}{4})}^{2} = \frac{81}{16}$
Hence, the correct answer is option a.

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Similar questions

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s e c θ - t a n θ = k,

then the value of

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s e c Θ - t a n Θ = \sqrt{2} t a n Θ,

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_____.

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If secθ−tanθ=45 and secθ+tanθ=m, then the value of (m+1)2 is equal to

The correct option is A Given : secθ−tanθ=45...(i)and, secθ+tanθ=m...(ii)Multiplying (i) and (ii), we get(secθ−tanθ)×(secθ+tanθ)=45×m⇒sec2θ−tan2θ=4m5⇒1=4m5 (∵1+tan2θ=sec2θ)⇒m=54∴ (m+1)2=(54+1)2=(94)2=8116 Hence, the correct answer is option a.

If $s e c θ - t a n θ = \frac{4}{5} a n d s e c θ + t a n θ = m,$ then the value of $(m + 1)^{2}$ is equal to