Show that sin 6 A -cos 6 A -1-3 sin 2 A -cos 2 A-

Here's your answer: As Cos^6A + sin^6A = gt;(Cos³A)² +( Sin³A)² = gt; (cos²A + sin²A ) ( Cos⁴A+ Sin⁴A Cos²A×Sin²A) = gt; Therefore [ a³ + b³ = (a+b ) ( ...

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Standard XII

Mathematics

Range of Trigonometric Expressions

show that sin...

Question

show that sin⁶A+cos⁶A=1-3sin²A.cos²A.

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Solution

Here's your answer:

As Cos^6A + sin^6A
=>(Cos³A)² +( Sin³A)²
=> (cos²A + sin²A ) ( Cos⁴A+ Sin⁴A - Cos²A×Sin²A)
=> Therefore [ a³ + b³ = (a+b ) ( a²+ b²-ab)]
=> (1 )(cos²A )² + (sin²A)² - 2cos²A× sin²A - cos²A× sin²A
=> [ a²+ b² =[ (a+b)² -2ab ]
=> 1²- 3sin²A×cos²A
=> 1 - 3sin²A×cos²A

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show that sin6A+cos6A=1-3sin2A.cos2A.

show that sin⁶A+cos⁶A=1-3sin²A.cos²A.