Answer:
cos65 = sin25 = p
tan205 = tan25 = p/√(1-√p)
Step-by-step explanation:
trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec)
some Trigonometric identities used in the question:
in the question it is given,
sin25 = p
using above mentioned identity:-
cos 65 = cos(90-25) = sin25 = p
hence value of cos65 is p.
for, tan205 we have to first find the cos25
so to find cos25 we use above mentioned identity,
cos²25 + sin²25 = 1
cos²25 + √p = 1
cos²25 = 1-√p
cos25 = √(1-√p)
now to find out tan205 use third identity mentioned above,
tan205 = tan(π+25) = tan25
tan25 = sin25/cos25
tan25 = p/√(1-√p)
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