Question

prove that sec theta - sin theta tan theta = cos theta​

Answer 1

Step-by-step explanation:

Knowing the facts, 1/secA = cosA

; tanA = sinA/cosA, given expression is:

=> secA - sinAtanA

=> 1/cosA - sinA(sinA/cosA)

=> 1/cosA - sin²A/cosA

=> (1 - sin²A)/cosA

=> (cos²A)/cosA {1 - sin²A = cos²A}

=> cosA

Answer 2

Answer:-

• To Prove:-

$\sf sec \theta - sin \theta tan \theta = cos \theta$

• Solution:-

$\sf sec \theta - sin \theta tan \theta = cos \theta$

Taking L.H.S:-

We know,

$\pink{\bigstar}$ $\boxed{\sf sec \theta = \dfrac{1}{cos \theta}}$

$\pink{\bigstar}$ $\boxed{\sf tan \theta = \dfrac{sin \theta}{cos \theta}}$

Now,

→ $\sf \dfrac{1}{cos \theta} - sin \theta \times \dfrac{sin \theta}{cos \theta}$

→ $\sf \dfrac{1}{cos \theta} - \dfrac{sin^2 \theta}{cos \theta}$

Taking LCM:-

→ $\sf \dfrac{1 - sin^2 \theta}{cos \theta}$

We know,

$\pink{\bigstar}$ $\boxed{\sf 1 - sin^2 \theta = cos^2 \theta}$

→ $\sf \dfrac{cos^2 \theta}{cos \theta}$

→ $\bf\large\blue{cos \theta}$

R.H.S = $\bf\large\blue{cos \theta}$

★ $\bf\large\green{cos \theta = cos \theta}$

L.H.S = R.H.S

★Hence Proved★