Question

Show that cot 405.tan-495 - tan 585.cot -495=0

Answer 1

Given: The term cot 405.tan-495 - tan 585.cot -495 = 0

To find: Prove LHS = RHS.

Solution:

• Now we have given the term cot 405.tan-495 - tan 585.cot -495 = 0

• Lets consider LHS, we have:

                  cot 405.tan-495 - tan 585.cot -495

• Now we know that :

                 tan (-x) = - tan x

                  cot (-x) = - cot x

• So applying this, we get:

                  { cot 405 x - (tan 495 )  } - { tan 585 x (-cot 495) }

• We can rewrite it as:

                  { cot(360 + 45) x - tan (540 - 45) } -  { tan (540 + 45) x - cot (540 - 45)  }

                  {  cot(45) x - tan (180 - 45) } -  { tan (180 + 45) x - cot (180 - 45)  }

                  (1 x -(- tan 45 )) - ( tan 45 x - (-cot 45) )

                  1 x 1 - (1 x 1)

                  1 - 1

                  0

Answer:

              So the value of given trigonometric term is 0.

Answer 2

Step-by-step explanation:

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