Question

please answer fast and correct ​

Answer 1

Answer:

Step-by-step explanation:

1. AB=25cm

let sin A=7/25

cos A=24/25

sinC=24/25

cosC=7/25

2. sint=1/2

t=30

cost=sqrt(3)/2

LHS:

3cost-4cos^3t=3sqrt(3)/2-(4)(3sqrt(3)/8)=0=RHS

3. when sinA=sinB

then value of A and B must be same

because

if A=90 then sinA=1

B=90 then sinB=1

LHS=RHS

so ang A=ang B

4. if tanA=1

A=45

sinA=1/sqrt2

cosA=1/sqrt(2)

2sinAcposA=2*(1/sqrt(2))(1/sqrt(2))=2*1/2=1=RHS

5. given x=cosecA+cosA

y=cosecA-cosA

x+y=2cosecA

x-y=2cosA

2/(x+y)=2/2cosecA=1/cosecA

(x-y)/2=2cosA/2=cosA

(2/x+y)^2+(x-y/2)^2=1/cosec^2A+cos^2A=sin^2A+cos^2A=1=RHS

6. x=cotA+cosA

y=cotA-cosA

x+y=2cotA

x-y=2cosA

(x-y/x+y)^2=(2cosA/2cotA)^2=sin^2A

(x-y/2)^2=cos^2A

LHS=sin^2A+cos^2A=1=RHS