The value of sin 765-cosec-1110-sin 405- 585- is equal to

The correct option is A 1As we know that 2π=360^∘ ∴sin 765^∘+cosec( 1110^∘) sin 405^∘+ 585^∘ =sin(4π+45°) cosec(6π+30°) sin(2π+45°)+(3π+45°) =sin(45°) cosec ...

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Standard XII

Mathematics

Trigonometric Ratios of Allied Angles

The value of ...

Question

The value of $sin 765^{\circ} + cosec (- 1110^{\circ}) - sin 405^{\circ} + cot 585^{\circ}$ is equal to

1

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Solution

The correct option is B $- 1$
As we know that $2 π = 360^{\circ}$
$∴ sin 765^{\circ} + cosec (- 1110^{\circ}) - sin 405^{\circ} + cot 585^{\circ}$

$= sin (4 π + 45 °) - cosec (6 π + 30 °) - sin (2 π + 45 °) + cot (3 π + 45 °)$

$= sin (45 °) - cosec (30 °) - sin (45 °) + cot (45 °)$

$= \frac{1}{\sqrt{2}} - 2 - \frac{1}{\sqrt{2}} + 1$

$= - 1$

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The value of sin765∘+cosec(−1110∘)−sin405∘+cot585∘ is equal to

The correct option is B −1As we know that 2π=360∘ ∴sin765∘+cosec(−1110∘)−sin405∘+cot585∘ =sin(4π+45°)−cosec(6π+30°)−sin(2π+45°)+cot(3π+45°) =sin(45°)−cosec(30°)−sin(45°)+cot(45°) =1√2−2−1√2+1 =−1

The value of $sin 765^{\circ} + cosec (- 1110^{\circ}) - sin 405^{\circ} + cot 585^{\circ}$ is equal to