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 

\[sec A \; =\; \frac{1}{cos A }\] 

\[tan A \; =\; \frac{sin A}{cos A }\] 

\[(secA+tanA)(1−sinA) \; = (\frac{1}{cosA} + \frac{sinA}{cosA}) \;(1−sinA) \]

\[\Rightarrow (\frac{1+sinA}{cosA})(1−sinA) \]

Now, let's expand this expression

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

\[\Rightarrow \frac{(1-sin^2A)}{cosA} \]

\[we\; know \;that \; { 1-cos^2A} \;=\; sin^2A, 💡  \]

\[\therefore \frac{(cos^2A)}{cosA} \; =\; cosA \]

Guess the Option and comment below  👇