Question

Prove that Sec0 (√1-sin²0)=1

Answer 1

Answer:

here your answer

Step-by-step explanation:

we know that

sec0=1

sin0=0

LHS

sec0(√1-sin^2 0)

1(√1-0^2)

1(√1)

1×1=1 RHS

Answer 2

Answer:

Hence proved : $sec\theta\sqrt{(1-sin^{2}\theta)}$ = 1

Step-by-step explanation:

We have to prove,

          $sec\theta\sqrt{(1-sin^{2}\theta)}$ = 1 --------------(i)

Take L.H.S from equation (i),

L.H.S = $sec\theta\sqrt{(1-sin^{2}\theta)}$ ----------------(ii)

Since $1-sin^{2}\theta=cos^{2}\theta$then equation (ii) becomes-

         = $sec\theta\sqrt{(cos^{2}\theta)}$

         = $sec\theta(cos\theta)$ --------------(iii)

where, $sec\theta=\dfrac{1}{cos\theta}$

Plugging this value in equation (iii) it becomes-

         = $\dfrac{1}{cos\theta}\times {cos\theta}$

         = 1

Which is equal to R.H.S of equation (i),

Hence,

          L.H.S = R.H.S