Question

evaluate (cosec theta-cot theta) = 1-cos theta/1+costheta​

Answer 1

Step-by-step explanation:

It has given that, sides of a right angled triangle are ; 6 cm, 8cm and 10 cm.

we have to find the length of perpendicular drawn to the hypotenuse from the opposite vertex.

solution : let length of perpendicular drawn to the hypotenuse is x cm.

let right angled triangle is ∆ABC where B is right angle. and we draw a perpendicular B to AC which touches AC at T.

here, ∠BAT = ∠BAC

and ∠BTA = ∠ABC

so, ∆ATB ~ ∆ABC

then, AB/AC = BT/BC

⇒6cm/10cm = BT/8 cm

⇒BT = 48/10 = 4.8 cm

Therefore the length of perpendicular drawn to hypotenuse is 4.8 cm

Answer 2

Answer:

LHS = RHS

Step-by-step explanation:

1- (1/Sin theta -cos theta / sin theta)^2

2- (1-cos theta/sin theta ) ^2 ( LCM)

3-(1-cos theta)^2/sin theta ^2

4- (1-cos theta)^2/ 1- cos^2 theta

5- (1- cos theta)^2/ (1)^2-(cos theta)^2 using a^2-b^2

6- (1-cos theta)^2/ (1+cos theta)(1-cos theta)

7- 1-cos theta / 1 + cos theta

hence proved

thanku