Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Updated On: 7-6-2020

Apne doubts clear karein ab Whatsapp par bhi. Try it now.

CLICK HERE

Loading DoubtNut Solution for you

Watch 1000+ concepts & tricky questions explained!

278.8 K+

13.9 K+

Text Solution

Solution :

`sinA = sin^2B ->(1)`<br>
`2cos^2A = 3cos^2B`<br>
`=>2cos^2A = 3(1-sin^2B)`<br>
From (1),<br>
`=>2(1-sin^2A) = 3(1-sinA)`<br>
`=>2sin^2A - 3sinA+1 = 0`<br>
`=>2sin^2A - 2sinA-sinA+1 = 0`<br>
`=>2sinA(sinA-1)-1(sinA-1) = 0`<br>
`=>(2sinA-1)(sinA-1) = 0`<br>
`=>sinA = 1 or sinA = 1/2`<br>
`=>A = 90^@ or A = 30^@`<br>
When `A = 90^@`, `sin^2B = 1 => B = 90^@`, which is not possible for a triangle.<br>
When `A = 30^@`, `sin^2B = 1/2 => B = 45^@`<br>
`=>C = (180-30-45)^@ = 75^@`<br>
`:. Delta ABC` is an obtuse angle triangle.<br>
So, option-`(b)` is the correct option.<br>
**Trigonometric equations and their solutions**

**(i) Prove that general solution of `sintheta=0` is given by `theta=npi; n in Z` (ii) Prove that general solution of `costheta=0` is `theta=((2n+1)pi/2); n in Z`**

**(iii)Prove that general solution of `tan theta=0` is `theta=npi; n in Z` (iv)Prove that the general solution of `cot theta=0` is `theta=(2n+1)pi/2, n in Z`**

**Prove that general solution of `sintheta=sin alpha` is given by `theta=npi+(-1)^n alpha, n in Z`**

**Find the general solution of the equations (i)`sin theta= sqrt3/2` (ii) `2sintheta+1=0` (iii)`cosectheta=2`**

**Prove that the general solution of `costheta=cosalpha`is given by `theta=2npipmalpha`; where `n inZ`**

**Find the general solution of the equation (i)`costheta=1/2 (ii) cos3theta=-1/2 (iii)sqrt3sec2theta=2`**

**Prove that general solution of `tan theta= tan alpha` is given by `theta=npi+alpha;n in Z`**

**Find the general solution of (i) `tan theta=1/sqrt3` (ii) `tan2theta=sqrt3` (iii)`tan3theta=-1`**

**General solution of `(i) sin^2theta = sin^2alpha; (ii) cos^2 theta = cos^2 alpha (iii) tan^2 theta = tan^2 alpha`**