Home
Class 10
MATHS
Prove that s e cA(1-sinA)(s e cA+t a nA)...

Prove that `s e cA(1-sinA)(s e cA+t a nA)=1`

Text Solution

AI Generated Solution

To prove the identity \( \sec A (1 - \sin A)(\sec A + \tan A) = 1 \), we will start with the left-hand side (LHS) and simplify it step by step. ### Step-by-Step Solution: 1. **Write down the LHS**: \[ \text{LHS} = \sec A (1 - \sin A)(\sec A + \tan A) \] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    NCERT|Exercise EXERCISE 8.3|7 Videos
  • INTRODUCTION TO TRIGONOMETRY

    NCERT|Exercise Exercise 8.2|4 Videos
  • COORDINATE GEOMETRY

    NCERT|Exercise EXERCISE 7.3|5 Videos
  • NCERT THEOREMS

    NCERT|Exercise THEOREM 10.1|2 Videos

Similar Questions

Explore conceptually related problems

Prove that: (1+cosA+sinA)/(1+cosA-sinA)=(1+sinA)/(cosA)

If a_1, a_2, a_n are in A.P. with common difference d!=0 , then the sum of the series sind[seca_1seca_2+(sec)_2seca_3+....+s e ca_(n-1)(sec)_n] is : a.cos e ca_n-cos e ca b. cota_n-cota c. s e ca_n-s e ca d. t a na_n-t a na

The expression (t a n A)/(1-cot A)+(cot A)/(1-t a n A) can be written as sin A cos A+1 b. s e c A\ cos e c A+1 c. t a n A+cot A d. s e c A+cos e c A

The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s e c A""cos e c A""+""1 (2) t a n A""+""cot A (3) s e c A""+""cos e c A (4) s in A""cos A""+""1

Incrircle of A B C touches the sides BC, CA and AB at D, E and F, respectively. Let r_1 be the radius of incricel of B D Fdot Then prove that r_1=1/2(s(-b)sinB)/((1+sinB/2))

Write the area of the triangle formed by the coordinate axes and the line (s e ctheta-t a ntheta)x+(s e ctheta+t a ntheta)y=2.

In the adjoining figure, BD||CA, E is the midpoint of CA and BD =(1)/(2) CA . Prove that ar(triangleABC)=2ar(triangleDBC) .

If a,b,c are in A.P. prove that: (i) (ab)^(-1),(ca)^(-1) and (bc)^(-1) are also in A.P. (ii) (ab+ac)/(bc),(bc+ca)/(ca),(ca+cb)/(ab) are also in A.P.

In the isosceles triangle ABC,|vec AB|=|vec BC|=8, a point E divide AB internally in the ratio 1:3, then the cosine of the angle between vec CE and vec CA is (where |vec CA|=12 )

Prove the relation, s_t=u + at - 1/2 a.