If 1-tan- a- what is the value of 2-2 tan- -A- a B- a2-1C- a 2D- a2-1

The correct option is C a^2It is given that, 1 tanθ=a Squaring boths sides, we get: (1 tanθ)^2=a^2 ⇒(1+tan^2θ 2tanθ)=a^2 Since 1+tan^2θ=^2θ, sec^2θ 2tanθ=a^2 ...

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Standard IX

Mathematics

Trigonometric Identities

If 1-tanθ= a,...

Question

If $1 - tan θ = a$ , what is the value of $s e c^{2} θ - 2 tan θ$ ?

a

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a^{2} - 1

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a^{2} + 1

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a^{2}

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Solution

The correct option is D $a^{2}$
It is given that, $1 - tan θ = a$
Squaring boths sides, we get:

$(1 - tan θ)^{2} = a^{2}$
$\Rightarrow$ $(1 + {tan}^{2} θ - 2 tan θ) = a^{2}$
Since $1 + {tan}^{2} θ = {sec}^{2} θ$ ,
$s e c^{2} θ - 2 tan θ = a^{2}$

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If 1−tanθ=a, what is the value of sec2θ−2tanθ ?

The correct option is D a2It is given that, 1−tanθ=a Squaring boths sides, we get: (1−tanθ)2=a2 ⇒(1+tan2θ−2tanθ)=a2 Since 1+tan2θ=sec2θ, sec2θ−2tanθ=a2

If $1 - tan θ = a$ , what is the value of $s e c^{2} θ - 2 tan θ$ ?

The correct option is D $a^{2}$
It is given that, $1 - tan θ = a$
Squaring boths sides, we get:

$(1 - tan θ)^{2} = a^{2}$
$\Rightarrow$ $(1 + {tan}^{2} θ - 2 tan θ) = a^{2}$
Since $1 + {tan}^{2} θ = {sec}^{2} θ$ ,
$s e c^{2} θ - 2 tan θ = a^{2}$