Question

If 2sin²theta - cos²theta =2 find the value of theta .

Answer 1

Step-by-step explanation:

2sin²a-2cos²a=2

2(sin²a-cos²a)=2

sin²a-cos²a=1

since sin²a+cos²a=1

sin²a-(1-sin²a)=1

2sin²a-1=1

2sin²a=2

sin²a=1

sin a=1

since sin 90⁰=1

therefore, a=90⁰

Answer 2

Step-by-step explanation:

$2 { \sin( \alpha ) }^{2} - { \cos( \alpha ) }^{2} = 2 \\ put \: cos { \alpha }^{2} = 1 - \sin( { \alpha }^{2} ) \\ 2 { \sin( \alpha ) }^{2} - (1 - { \sin( \alpha )) }^{2} = 2 \\ 3 \sin( {\alpha }^{2} ) = 3 \\ \sin( { \alpha }^{2} ) = 1 \\ \sin( \alpha ) = + - 1 \\ \alpha = + - \pi \div 2$