Question

If root5tantheeta=5sintheeta find the value of sin squaretheeta -- cos squaretheeta

Answer 1

√5tanФ=5sinФ (assuming, theeta=Ф)
or, sinФ/cosФ=(5/√5)sinФ
or, 1/cosФ=√5sinФ/sinФ
or, 1/cosФ=√5
or, cosФ=1/√5
∴, cos²Ф=1/5
∵, sin²Ф+cos²Ф=1
then, sin²Ф=1-cos²Ф=1-1/5=4/5
∴, sin²Ф-cos²Ф=4/5-1/5=3/5