Question

(secx+tanx) (1-sinx)=?​

Answer 1

To Solve

→ (secx + tanx)(1 - sinx)

Solution

→ (secx + tanx)(1 - sinx)

→ (1/cosx + sinx/cosx)(1 - sinx)

→ (1 + sinx)/cosx × (1 - sinx)

→ (1 - sin²x)/cosx

→ cos²x/cosx

→ cosx

Identities used

• tan∅ = sin∅/cos∅
• sec∅ = 1/cos∅
• (a + b)(a - b) = a² - b²
• 1 - sin²∅ = cos²∅

Answer: cosx

Answer 2

$\huge\boxed{Answer:-}$

$\boxed{Answer=cosx}$

Explanation:

Let us find the answer for (secx+tanx) (1-sinx)=?

$=>(secx + tanx)(1 - sinx)$

$=>( \frac{1}{cosx} + \frac{sinx}{cosx} )(1 - sinx)$

$=> \frac{(1 + sinx)}{cosx} × (1 - sinx)$

$=>\frac{(1 - sin2x)}{cosx}$

=>(cos²x)/(cosx°cosx)

identies we used to get our answer:

• tan° = sin°/cos°
• sec° = 1/cos°
• (a + b)(a - b) = a² - b²
• 1 - sin²° = cos²°

Proved!!

Therefore (secx+tanx) (1-sinx)=(cosx)