If x - sec - - tan - y - cosec - - cot - then xy - 1-

Xy+1 = (sec θ tan θ)(cosec θ + cot θ)+1 =(1 sin θcos θ) (1 + cos θsin θ)+1 =1+cos θ sin θ sin θ cos θ + sin θ cosθsin θ cos θ =1+cos θ sin θsin θ cos ...

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Byju's Answer

Standard XII

Physics

Introduction

If x = sec θ ...

Question

If $x = s e c θ - t a n θ, y = c o s e c θ + c o t θ$ , then $x y + 1 =$ _____

x + y

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x - y

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y - x

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- x - y

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Solution

The correct option is C $y - x$
$x y + 1 = (s e c θ - t a n θ) (c o s e c θ + c o t θ) + 1$
$= (\frac{1 - s i n θ}{c o s θ}) (\frac{1 + c o s θ}{s i n θ}) + 1$
$= \frac{1 + c o s θ - s i n θ - s i n θ c o s θ + s i n θ c o s θ}{s i n θ c o s θ}$
$= \frac{1 + c o s θ - s i n θ}{s i n θ c o s θ}$
$= \frac{s i n^{2} θ + c o s^{2} θ + c o s θ - s i n θ}{s i n θ c o s θ}$
$= t a n θ + c o t θ + c o s e c θ - s e c θ$
$= (c o t θ + c o s e c θ) - (s e c θ - t a n θ)$
$= y - x$

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If x=secθ−tanθ,y=cosecθ+cotθ, then xy+1= _____

The correct option is C y−xxy+1=(secθ−tanθ)(cosecθ+cotθ)+1 =(1−sinθcosθ)(1+cosθsinθ)+1 =1+cosθ−sinθ−sinθ cosθ+sinθ cosθsinθ cosθ =1+cosθ−sinθsinθ cosθ =sin2θ+cos2θ+cosθ−sinθsinθ cosθ =tanθ+cotθ+cosecθ−secθ =(cotθ+cosecθ)−(secθ−tanθ) =y−x

If $x = s e c θ - t a n θ, y = c o s e c θ + c o t θ$ , then $x y + 1 =$ _____