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

As we know that 2π=360^∘ ∴sin 765^∘+cosec( 1110^∘) sin 405^∘+ 585^∘ =sin(4π+ π4) cosec(6π+π6) sin(2π+π4)+ (3π+π4) =sin(45°) cosec(30°) sin(45°)+(45°) =1√(2) ...

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Standard XIII

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 $2 π = 360^{\circ}$
$∴ sin 765^{\circ} + cosec (- 1110^{\circ}) - sin 405^{\circ} + cot 585^{\circ}$

$= sin (4 π + \frac{π}{4}) - cosec (6 π + \frac{π}{6}) - sin (2 π + \frac{π}{4}) + cot (3 π + \frac{π}{4})$

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

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

$= - 1$

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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+π4)−cosec(6π+π6)−sin(2π+π4)+cot(3π+π4) =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