Question

sec 840º.cot (- 945°) + sin 600° tan (-690°)=3/2​

Answer 1

Step-by-step explanation:

x

2

+y

2

=(asinθ+ccosθ)

2

+(acosθ−csinθ)

2

=a

2

sin

2

θ+c

2

cos

2

θ+2acsinθcosθ+a

2

cos

2

θ+c

2

sin

2

θ−2acsinθcosθ

=a

2

(sin

2

θ+cos

2

θ)+c

2

(sin

2

θ+cos

2

θ)

=a

2

+c

2

Answer 2

Step-by-step explanation:

sin600×tan(−690)+sec840×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}−

2

3

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}−

3

1

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)sin600×tan(−690)+sec840×cot(−945)

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

2

3

×−

3

1

+−2×−1

\frac{1}{2} + 2

2

1

+2

\frac{5}{2}

2

5