Question

Evaluate cos225-sin225-tan495-cot495 ​

Answer 1

Consider,cos225

∘

−sin225

∘

=cos(180

∘

+45

∘

)−sin(180

∘

+45

∘

)

=−cos45

∘

+sin45

∘

=−

2

1

+

2

1

=0

=

2

−2

×

2

2

=

2

−2

2

=−

2

Consider tan495

∘

−cot495

∘

=tan495

∘

−cot495

∘

=tan(5×90

∘

+45

∘

)−cot(5×90

∘

+45

∘

)

Here n=5 is odd , so tan changes to cot and cot changes to tan

=−cot45

∘

−(−tan45

∘

) since 495

∘

=5×90

∘

+45

∘

is in second quadrant,hence tan495

∘

is negative.

=−1+1=0

∴cos225

∘

−sin225

∘

+tan495

∘

−cot495

∘

=0−

2

=−

2

Answer 2

Answer:

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