a) Find the value of m if sec65∘=cosec(2m−15)∘
m=20
Step 1 :Given that sec65∘=cosec(2m−15)∘
Step 2 :Using the identities secx=1cosx and cosecx=1sinx, we get 1cos65∘=1sin(2m−15)∘
Step 3 :Using the identity sin(2x)=2sinxcosx, we can rewrite the equation as 1cos65∘=12sin(m−7.5∘)cos(m−7.5∘)
Step 4 :Solving for m, we get m=20
Step 5 :m=20