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 follow these steps: ### Step 1: Convert secant and tangent to sine and cosine We know that: \[ \sec A = \frac{1}{\cos A} \quad \text{and} \quad \tan A = \frac{\sin A}{\cos A} \] Substituting these into the left-hand side (LHS) of the equation gives: ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    NCERT ENGLISH|Exercise Exercise 8.1|11 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NCERT ENGLISH|Exercise EXERCISE 8.3|7 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NCERT ENGLISH|Exercise Exercise 8.4|14 Videos

  • COORDINATE GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 7.3|5 Videos

  • NCERT THEOREMS

    NCERT ENGLISH|Exercise THEOREM 10.1|2 Videos

Similar Questions

Explore conceptually related problems

Prove: (cos e c\ A-sinA)(secA-cosA)(tanA+cotA)=1

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

Prove that: " "( tan A + sinA)/(tanA - sinA) = (sec A +1)/(secA -1)

Prove that: 2s e c^2theta-s e c^4theta-2cos e c^2theta+cos e c^4theta=(1-t a n^8theta)/(t a n^4theta)

Prove that : sqrt((1+sinA)/(1-sinA))-sqrt((1-sinA)/(1+sinA))=2tanA

Prove: 1/(1+sinA)+1/(1-sinA)=2sec^2A

Prove the following identity: (s e c A\ s e c B+t a n AtanB)^2-(s e c A\ t a n B+t a n A s e c B)^2=1

If tan^2theta=1-a^2, prove that s e ctheta+tan^3thetacos e ctheta=(2-a^2)^(3/2)

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+seca_2seca_3+....+s e ca_(n-1)seca_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

Prove that (cotA-cosA)/(cotA+cosA)=(c o s e cA-1)/(c o s e cA+1) .

Home
Profile