Class X Session 2023-24 Question 12

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041) 

Question 12

(sec A + tan A) (1 – sin A) equals :

(a) sec A 

(b) sin A 

(c) cosec A 

(d) cos A

Explanation : 

let's first express  sec A and tan A in terms of sinA and cos A

We know that 

$$secA=\frac{1}{cosA}$$ 

$$tanA=\frac{sinA}{cosA}$$ 

$$(secA+tanA)(1-sinA)=(\frac{1}{cosA}+\frac{sinA}{cosA})(1-sinA)$$

$$\Rightarrow (\frac{1+sinA}{cosA})(1-sinA)$$

Now, let's expand this expression

$$\Rightarrow \frac{(1+sinA)(1-sinA)}{cosA}$$

$$\Rightarrow \frac{(1-si{n}^{2}A)}{cosA}$$

$$weknowthat1-co{s}^{2}A=si{n}^{2}A,💡$$

$$\therefore \frac{(co{s}^{2}A)}{cosA}=cosA$$

Guess the Option and comment below  👇