Question

find the value of cos-(1410)°

Answer 1

Let us first convert angle given in degree to radian:

−1410°=−1410(π/180)=−(47/3)π=−(8–1/6)π−1410°=−1410(π/180)=−(47/3)π=−(8–1/6)π

So,
cosec(−1410°)=cosec(−8–1/6π)cosec(−1410°)=cosec(−8–1/6π)

# cosec(−x)=−cosec(x)cosec(−x)=−cosec(x), then:

cosec(−1410)=−cosec(8–1/6π)cosec(−1410)=−cosec(8–1/6π)

cosec(−1410)=−cosec(8–1/6π)cosec(−1410)=−cosec(8–1/6π)

#As we know that after an interval of 2π, values ofcoseccosecrepeat. Then:

cosec(−1410)=−cosec(8–1/6π)cosec(−1410)=−cosec(8–1/6π)

cosec(−1410)=−cosec(–1/6π)cosec(−1410)=−cosec(–1/6π)

cosec(−1410)=cosec(1/6π)cosec(−1410)=cosec(1/6π)

cosec(−1410)=cosec(30°)cosec(−1410)=cosec(30°)

cosec(−1410)=1/sin(30°)cosec(−1410)=1/sin(30°)

cosec(−1410)=1/(1/2)cosec(−1410)=1/(1/2)

cosec(−1410)=2cosec(−1410)=2

is the solution.

Hope it helps........!

Answer 2

Answer:

cosec(-1410)

-cosec(4×360-30)

cosec30°=2