Check if -2- - -sin- - -cos2- - -sin- - -tan2- - -

( π2+ θ) ).sin( θ).(π θ)cos(2π θ).sin(π + θ).tan(2π θ)= cosec θ ( tanθ)( sinθ)( θ)(cosθ)( sinθ)( tanθ)= cosec θ θcosθ=cosec θ 1cosθ×c ...

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Standard X

Mathematics

Trigonometric Ratios

Check if π2...

Question

Check if $\frac{cot (\frac{π}{2} + θ) . sin (- θ) . (cot π - θ)}{cos (2 π - θ) . sin (π + θ) . tan (2 π - θ)} = - csc θ$

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Solution

$\frac{cot (\frac{π}{2} + θ)) . sin (- θ) . (cot π - θ)}{cos (2 π - θ) . sin (π + θ) . tan (2 π - θ)} = - c o s e c θ$

$\frac{(- tan θ) (- sin θ) (- cot θ)}{(cos θ) (- sin θ) (- tan θ)} = - c o s e c θ$

$\frac{cot θ}{cos θ} = c o s e c θ$

$\frac{1}{cos θ} \times \frac{cos θ}{sin θ} = \frac{1}{sin θ}$

$1 = 1$

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Similar questions

c o s^{2} (\frac{π}{2} + θ) - s i n^{2} (\frac{π}{2} - θ) =

Q. The value of

cot (\frac{π}{4} + θ) . cot (\frac{π}{4} - θ)

Prove that:

$(i) \frac{c o s (2 π + θ) c o s e c (2 π + θ) t a n (π / 2 + θ)}{s e c (π / 2 + θ) c o s θ c o t (π + θ)} = 1$

$(i i) \frac{c o s e c (90^{\circ} + θ) + c o t (450^{\circ} + θ)}{c o s e c (90^{\circ} - θ) + t a n (180^{\circ} - θ)} + \frac{t a n (180^{\circ} + θ) + s e c (180^{\circ} - θ)}{t a n (360^{\circ} + θ) - s e c (- θ)} = 2$

$(i i i) \frac{s i n (180^{\circ} + θ) c o s (90^{\circ} + θ) t a n (270^{\circ} - θ) c o t (360^{\circ} - θ)}{s i n (360^{\circ} - θ) c o s (360^{\circ} + θ) c o s e c (- θ) s i n (270^{\circ} + θ)} (i v) 1 + c o t θ - s e c (\frac{π}{2} + θ)} 1 + c o t θ + s e c (\frac{π}{2} + θ)} = 2 c o t θ$

$(v) \frac{t a n (90^{\circ} - θ) s e c (180^{\circ} - θ) s i n (- θ)}{s i n (180^{\circ} + θ) c o t (360^{\circ} - θ) c o s e c (90^{\circ} - θ)} = 1$

Q. If

tan θ - i,

where

θ \in (- \frac{π}{2}, \frac{π}{2})

can be written as

r e^{i β}

, then

(r, β)

cos θ + cos (π + θ) + cos (2 π + θ) + \dots + 2 n

terms =

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Check if cot(π2+θ).sin(−θ).(cotπ−θ)cos(2π−θ).sin(π+θ).tan(2π−θ)=−cscθ

cot(π2+θ)).sin(−θ).(cotπ−θ)cos(2π−θ).sin(π+θ).tan(2π−θ)=−cosecθ(−tanθ)(−sinθ)(−cotθ)(cosθ)(−sinθ)(−tanθ)=−cosecθcotθcosθ=cosecθ1cosθ×cosθsinθ=1sinθ1=1

Check if $\frac{cot (\frac{π}{2} + θ) . sin (- θ) . (cot π - θ)}{cos (2 π - θ) . sin (π + θ) . tan (2 π - θ)} = - csc θ$