Question

यदि sinx + cosx = a, तो sin⁶x + cos⁶x = ______

Answer 1

समझें कि दी गई अभिव्यक्ति है sinx + cosx = a

दोनों पक्षों को वर्ग,

∴ `sin^2x + cos^2x + 2sinx cosx = a^2`

⇒ 1 + 2sinx cosx = a²

⇒ sinx cosx = `(a^2 - 1)/2`

गणना `sin^6 + cos^6x`

∴ `sin^6x + cos^6x = (sin^2x)^3 + (cos^2x)^3`

⇒ `sin^6x + cos^6x = (sin^2x + cos^2x) - 3sin^2x cos^2x(sin^2x + cos^2x)`

= `1 - 3((a^2 - 1)/2)^2 . 1`

= `1/4[4 - 3(a^2 - 1)^2]`