Simplify 90- -sin 90- - -cos-tan 90- - - - -

( 90 #176; θ #160; ) #160; #160; sin( 90 #176; θ #160; ) #160; #160; ×cosθ #160; #160; tan( 90 #176; θ #160; ) #160; #160; ...

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Standard X

Mathematics

Trigonometric Identities

Simplify 90...

Question

Simplify $\frac{sec (90^{\circ} - θ)}{sin (90^{\circ} - θ)} \times \frac{cos θ}{tan (90^{\circ} - θ)} - sec θ$

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Solution

$\frac{sec (90 ° - θ)}{sin (90 ° - θ)} \times \frac{cos θ}{tan (90 ° - θ)} - sec θ = \frac{c o s e c θ}{cos θ} + \frac{cos θ}{cot θ} - sec θ$
$= \frac{1}{sin θ} \times \frac{sin θ}{cos θ} - sec θ$
$= \frac{1}{cos θ} - sec θ$
$= \frac{1}{cos θ} - sec θ$
$= sec θ - sec θ$
$= 0$
Hence, the answer is $0.$

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Similar questions

Q. Evaluate

\frac{cos θ}{sin (90 + θ)} + \frac{sin (- θ)}{sin (180 + θ)} + \frac{tan (90 + θ)}{cot θ}

Prove that:

(i) $s i n θ c o s (90^{\circ} - θ) + s i n (90^{\circ} - θ) c o s θ = 1$

(ii) $\frac{s i n θ}{c o s (90^{\circ} - θ)} + \frac{c o s θ}{s i n (90^{\circ} - θ)} = 2$

(iii) $\frac{s i n θ c o s (90^{\circ} - θ) c o s θ}{s i n (90^{\circ} - θ)} + \frac{c o s θ s i n (90^{\circ} - θ) s i n θ}{c o s (90^{\circ} - θ)} = 1$

(iv) $\frac{c o s (90^{\circ} - θ) s e c (90^{\circ} - θ) t a n θ}{c o s e c (90^{\circ} - θ) s i n (90^{\circ} - θ) c o t (90^{\circ} - θ)} + \frac{t a n (90^{\circ} - θ)}{c o t θ} = 2$

(v) $\frac{c o s (90^{\circ} - θ)}{1 + s i n (90^{\circ} - θ)} + \frac{1 + s i n (90^{\circ} - θ)}{c o s (90^{\circ} - θ)} = 2 c o s e c θ$

(vi) $\frac{s e c (90^{\circ} - θ) c o s e c θ - t a n (90^{\circ} - θ) c o t θ + c o s^{2} 25^{\circ} + c o s^{2} 65^{\circ}}{3 t a n 27^{\circ} t a n 63^{\circ}} = \frac{2}{3}$

(vii) $c o t θ t a n (90^{\circ} - θ) - s e c (90^{\circ} - θ) c o s e c θ + \sqrt{3} t a n 12^{\circ} t a n 60^{\circ} t a n 78^{\circ} = 2$

Q. The value of

\frac{cos Θ}{sin (90 + Θ)} + \frac{sin (- Θ)}{sin (180 + Θ)} + \frac{tan (90 + Θ)}{cot Θ}

Q. The value of :

\frac{c o s θ}{s i n (90 + θ)} + \frac{s i n (- θ)}{s i n (180 + θ)} + \frac{t a n (90 + θ)}{c o t θ}

Q. If

sin (90 - θ) + cos θ = \sqrt{2} cos (90 - θ)

, for

0 < θ < 90^{\circ}

, find the value of

cosec θ

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Simplify sec(90∘−θ)sin(90∘−θ)×cosθtan(90∘−θ)−secθ

sec(90°−θ)sin(90°−θ)×cosθtan(90°−θ)−secθ=cosecθcosθ+cosθcotθ−secθ =1sinθ×sinθcosθ−secθ =1cosθ−secθ =1cosθ−secθ =secθ−secθ =0Hence, the answer is 0.

Simplify $\frac{sec (90^{\circ} - θ)}{sin (90^{\circ} - θ)} \times \frac{cos θ}{tan (90^{\circ} - θ)} - sec θ$