Question

Q.8
If cot^3a + cot^2a + cot a=1 then
(A) cos 2a.tan a=-1
(B) cos 2a.tana=1
(C) cos2a - tan2a=1
(D) cos 2a - tan 2a =-1​

Answer 1

answer : option (A) cos2a.tana = -1

it is given that , cot³a + cot²a + cota = 1

or, cos³a/sin³a + cos²a/sin²a + cosa/sina = 1

or, cos³a/sin³a + cosa/sina = 1 - cos²a/sin²a

or, cosa/sina [ cos²a/sin²a + 1] = (sin²a - cos²a)/sin²a

or, cosa/sina [cos²a + sin²a ]/sin²a = -(cos²a - sin²a)/sin²a

we know, cos²x - sin²x = cos2x

so, cos²a - sin²a = cos2a

also, sin²x + cos²x = 1

so, sin²a + cos²a = 1

now, cosa/sina × 1/sin²a = -cos2a/sin²a

or, cosa/sina = -cos2a

or, cota = -cos2a

or, 1 = -cos2a. 1/cota

or, -1 = -cos2a.tana

hence, option (A) is correct choice.

Answer 2

Answer:

option a

Step-by-step explanation:

the direction of a motion of a projectile at a certain instant is inclined at an angle a to the horizontal. After t second inclined at an angle b. find the horizontal component of velocity of projection in term of g,t,a and b (a and b are positive angle in anticlockwise direction