Question

sec2 tetha -tan 2 theta =1 prove it​

Answer 1

Answer:

Taking LHS=sec

2

θ+cosec

2

θ

=

cos

2

θ

1

+

sin

2

θ

1

[∵cosθ=

secθ

1

];[sinθ=

cosecθ

1

]

=

cos

2

θsin

2

θ

sin

2

θ+cos

2

θ

[∵cos

2

θ+sin

2

θ=1]

=

cos

2

θsin

2

θ

1

=sec

2

θ.cosec

2

θ=RHS[∵cosθ=

secθ

1

];[sinθ=

cosecθ

Answer 2

$\Large{\underline{\underline{\bold{✯Required\;To\;Prove:}}}}$

• $\sf{sec²\theta-tan²\theta = 1}$

$\Large{\underline{\underline{\blue{\bold{➸Proof:}}}}}$

$→\;{\sf{sec²\theta-tan²\theta}}$

$→\;\Large{\sf{\frac{1}{cos²\theta}-\frac{sin²\theta}{cos²\theta}}}$

$→\;\Large{\sf{\frac{1-sin²\theta}{cos²\theta}}}$

• $\boxed{\pink{\sf{sin²\theta-cos²\theta = 1}}}$
• $\boxed{\pink{\sf{cos²\theta = 1-sin²\theta}}}$

$→\;\Large{\sf{\cancel{\frac{cos²\theta}{cos²\theta}}}}$

$→\;{\bold{1}}$

Hence, Proved

• $\Large{\red{\bold{sec²\theta-tan²\theta = 1}}}$

$\Large{\tt{@Mr Sovereign}}$

Hope This Helps!!