Question

Explain it plzz With explanation give your ans in less than 3 hours to get brainliest ...

question posted 6 23 pm ​

Answer 1

Answer:

Hey there

Pls refer below for the soln of ur asked query

Step-by-step explanation:

If sin theta= sin alpha

then general soln for theta = nπ + (-1)^n (alpha) n€I

Applying this here

Given Alpha= π/4

Means

sin theta = sin alpha

= sin (π/4)

= 1/√2

Thus, Value of the given Expression is (B)

Hope it clears ur doubts

Answer 2

Answer:

b) 1/√2

Step-by-step explanation:

the given solution is the general solution of sinx. this solution is equivalent to sinπ/4 no matter what n is and the value of sin π/4 is 1/√2.

let us discuss how this general solution is formed.

the angle x ishould be measured w.r.t positive x axis anticlockwise. but we generally solve x in the range between 0 and 90. so when x is in first quadrant, it is measured anticlockwise w.r.t positive x axis and hence x=x. when it is in second quadrant, it is measured clockwise w.r.t negative x axis. hence actual x is π-x. similarly in third quadrant acute x is measured anticlockwise w.r.t negative x axis. hence actual x is π+x. in fourth quadrant acute x is measured clockwise w.r.t positive x axis. hence actual x is 2π-x. After one rotation x reaches in first quadrant again where x = 2π+x. thus rotating an angle by multiple of 2π does not make any difference.

now sinx is positive in first and second quadrant. hence when you find a solution of sinx in positive x, it is either in first or second quadrant. the general solution takes care of this see how

sinx= nπ + (-1)^n x

put n= 0 and solution is sinx

put n=1 and solution is sin(π-x) which is again sinx (second quadrant, sin positive)

put n= 2 and solution is sin(2π+x) which is sinx as discussed above.(rotating by 2π does not make any difference)

put n = 3 and solution is sin(3π-x) = sin (2π+π-x) = sin(π-x) = sinx

thus, we can see the solution is sinx for every x. the general solution of a trigonometrical ratio is used to find all the angles for which the value of trigonometrical ratio is equal to its value in respect of the acute angle.

hope I was clear enough and you find it useful