Sinx=cosy hole cosec(x+y)er man kata?

No idea what you are saying.

your question is not readable

Dekhiye, aapne ek mathematical expression diya hai: sinx = cosy / cosec(x+y). Ab yahan, hume sinx aur cosy ko related karne ke liye trigonometric identities ka istemal karna hoga.

Trigonometric identities hume ek angle ke trigonometric functions ko dusre angle ke trigonometric functions me convert karne mein madad karti hai. Is equation mein, hume sinx ko cosy ke saath relate karna hai. Iske liye hum cosine ka reciprocal, yaani cosec ka istemal karenge.

So, cosec(x) = 1/sinx aur cosec(y) = 1/cosy, isko equation mein daal kar humara equation ban jaata hai:

1/sinx = cosy / (1/sinx + 1/cosy)

Yahaan hume x+y ke place par y daalna hai:

1/sinx = cosy / (1/sinx + 1/cos(y))

Is equation me humara goal hai sinx ko cosecy ke saath relate karna. Is equation ko solve karne ke liye, hume equation ke dono taraf ko sinx se multiply kar dena hai:

1 = cosy * sinx / (1 + sin(x) * sin(y) / cos(y))

Yahaan par cos(x+y) ki jagah par hum cos(x) * cos(y) - sin(x) * sin(y) ko istemal karenge kyunki cos(x+y) = cos(x) * cos(y) - sin(x) * sin(y) hai.

So, is equation ko likhte hain:

1 = cosy * sinx / (1 + sin(x) * sin(y) / cos(y))

1 = cosy * sinx / (1 + cos(x)*cos(y) - sin(x)*sin(y) / cos(y))

Dekhiye, humara equation ab cos(x) * cos(y) aur sin(x) * sin(y) ke terms ko contain kar raha hai. Agar hum inhe yahaan se cancel out kar dein, toh humare pass acosine aur sine term hi bachenge.

1 = cosy / (cos(x))

cosy = cos(x)

Yahaan humara answer aaya hai, cosy = cos(x). Yani ki, sinx = cosy ka matlab hai ki sinx = cos(x).