Question

If 7 sin α = 24 cos α where 0° < < 90°, then value of

14 tan – 75 cos – 7 sec is equal to :

(A) 1 (B) 2

(C) 3 (D) 4​

Answer 1

Given :  7 sin α = 24 cos α where 0° < α< 90°,  

To find : 14 tanα – 75 cosα – 7 secα

Solution:

7 sin α = 24 cos α

=>  sin α / cos α   = 24/7

=> tan α = 24/7

Sec²α = tan²α + 1

=> Sec²α = (24/7)²+ 1

=> Sec²αα = (25/7)²   ( ∵24² + 7² = 25)

=> Secα = 25/7     ( ∵  0° < α< 90°,  hence only positive value possible )

Cosα  = 7/25

14 tanα – 75 cosα – 7 secα

= 14(24/7) - 75 (7/25) - 7 (25/7)

= 48 - 21 - 25

= 2

14 tanα – 75 cosα – 7 secα  = 2

option B is correct

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Answer 2

Answer:

2 be the correct option in this question solution are there