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abhishek chaudhary

· started a discussion

· 1 Months ago

query (Question: 186119.0 )

explain second step please

Question:
If sec\(\theta\) + tan\(\theta\) = 4, (\(\theta\neq\) 90º), then the value of cos\(\theta\) is – 
Options:
A) 0
B) \(\cfrac{8}{17}\)
C) \(\cfrac{17}{8}\)
D) \(\cfrac{4}{5}\)
Solution:
Ans: (b) Sec\(\theta\) + tan\(\theta\)  = 4 

sec\(\theta\) - tan\(\theta\)  = \(\cfrac{1}{4}\)

2 sec\(\theta\) = 4 + \(\cfrac{1}{4} = \cfrac{17}{4}\)

sec \(\theta\)= \(\cfrac{17}{8}\)

cos\(\theta\) = \(\cfrac{8}{17}\)

Pranay SB

· commented

· 1 Months ago

s1: sec Q + tan Q =4-------------------------------(1)
s2: sec^2 Q - tan^2 Q=1 (identity)
s3: (sec Q+tanQ)(sec Q-tanQ)=1
s4: 4 (sec Q-tanQ)=1 ; so -> secQ - tanQ=1/4 ----(2) solving 1 & 2 you will get what cosQ is

Knowledge Expert

· commented

· 1 Months ago

Since, secθ + tanθ = 4

(secθ + tanθ )(secθ - tanθ)/(secθ - tanθ) = 4

(sec^2θ - tan^2θ)/(secθ - tanθ) = 4

Since, sec^2θ - tan^2θ = 1

so, 1/(secθ - tanθ) = 4

so, 1/4 = (secθ - tanθ)
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