Question

if cosec theta+cot theta=a then find the value of 2 cosec theta+3 cot theta

Answer 1

Answer:

Step-by-step explanation:

Answer 2

given: cosec theta+cot theta=a °°°°°°°《1》

to find: the value of 2 cosec theta+3 cot theta

solution:

formula: 1 + cot^2 theta = cosec^2 theta

cosec^2 theta - cot^2 theta = 1
(cosec theta + cot theta )(cosec theta - cot theta) =1 [by the formula of a^2 - b^ ]

a(cosec theta- cot theta ) = 1 (from 1 )

cosec theta - cot theta = 1/ a ....(2)

solving 1 and 2
cosec theta+cot theta=a
cosec theta - cot theta = 1/ a
________________________
2 cosec theta = a+ 1/a
= (1+a^2)/ a ...........(3) (by adding)
multiplying by 3 in 1 and 2
we obtain

3 cosec theta + 3 cot theta = 3a
3cosec theta - 3 cot theta = 3/a
________________________
6 cot theta = 3a- 3/a (by subtraction )
6 cot theta = (3a^2 -3) /a
devinded by 2 in both side (in the question we should 3 cot theta not 6 cot theta so we divide by 2)

3 cot theta =(3a^2 -3) /2a .......(4)
according to question
2 cosec theta + 3cot theta = (1+a^2)/ a + (3a^2 -3) /2a
=[2(a^2+1)+ 3(a^2-1)] / 2a
= (2a^2 + 2 +3a^2-3 ) / 2a
=(5a^2 - 1 ) / 2a
hope it will help u
Mark it brainly