cos⁴theta-sin⁴theta =2cos²theeta-1
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Answer:
=> cos^4 theeta - sin^4theeta
- sin^4theeta can be written as
( sin^2theeta)^2
=> (sin^2theeta)^2 = (1 - cos^2theeta)^2
=> cos^4 theeta - (1 - cos^2theeta)^2
- ( 1 - cos^2theeta)^2 = ( 1 + cos^4 theeta -
2cos^2theeta
=> cos^4 theeta- ( 1 + cos^4 theeta - 2cos^2theeta)
=>2cos^2theeta - 1
Hence Proved.
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