The value of cos-sin 90- -sin-sin 180- - 90- -tan- is

The correct option is A 1 sin(90^∘ +θ)= cos θ sin(180^∘ +θ)= sin θ cot(90^∘ θ)= tan θ Using these identities we get 1 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Iota

the value of ...

Question

the value of $\frac{c o s Θ}{sin (90^{\circ} + Θ)} + \frac{sin}{sin (180^{\circ} + Θ)} + \frac{cot (90^{\circ} - Θ)}{tan Θ}$ is

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Solution

The correct option is A 1
$s i n (90^{\circ} + θ) = c o s θ$
$s i n (180^{\circ} + θ) = - s i n θ$
$c o t (90^{\circ} - θ) = t a n θ$
Using these identities we get 1

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Similar questions

Q. The value of

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

Q. Evaluate

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

Q. Simplify

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

Q. If

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

, for

0 < θ < 90^{\circ}

, find the value of

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

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the value of cosΘsin(90∘+Θ)+sinsin(180∘+Θ)+cot(90∘−Θ)tanΘ is

The correct option is A 1sin(90∘+θ)=cosθsin(180∘+θ)=−sinθcot(90∘−θ)=tanθUsing these identities we get 1

the value of $\frac{c o s Θ}{sin (90^{\circ} + Θ)} + \frac{sin}{sin (180^{\circ} + Θ)} + \frac{cot (90^{\circ} - Θ)}{tan Θ}$ is

The correct option is A 1
$s i n (90^{\circ} + θ) = c o s θ$
$s i n (180^{\circ} + θ) = - s i n θ$
$c o t (90^{\circ} - θ) = t a n θ$
Using these identities we get 1