Question

4. sin 600 * tan (-690) + sec 840 * cot(-945)

Answer 1

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Answer 2

Answer:

$\frac{5}{2}$

Step-by-step explanation:

In this question

$sin 600\times tan (-690) + sec 840\times cot (-945)$

So, sin 600 = sin(360 + 240)

     sin 600 = sin 240 = sin (180 + 60)

     sin 600 = -sin 60

     sin 600 = $-\frac{\sqrt 3}{2}$

tan (-690) = - tan 690

tan (-690) = - tan(360 + 330)

tan (-690) = - tan 330 = - tan (270 + 60)

tan (-690) = - cot 60

tan (-690) = $-\frac{1}{\sqrt 3}$

sec 840 = sec (720 + 120)

sec 840 = sec 120 = sec (90 + 30)

sec 840 = - cosec 30

sec 840 = -2

cot (-945) = - cot 945 = - cot (720 + 225)

cot (-945) = - cot 225 = - cot (270 - 45)

cot (-945) = - cot 45 = -1

Now, we can putting all the value in equation

$sin 600\times tan (-690) + sec 840\times cot (-945)$

$-\frac{\sqrt 3}{2}\times -\frac{1}{\sqrt 3}+ -2\times-1$

$\frac{1}{2} + 2$

$\frac{5}{2}$